Asked by Stranger danger
bot what does $(4^3 \cdot 7^{-2})^{-5}/7^9 \cdot mean?
Answers
Answered by
Stranger danger
Apply the Properties of Integer Exponents to generate equivalent expressions to (4^3 ⋅ 7^-2)^-5/79 ⋅ 4^-13 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
Answered by
Stranger danger
Apply the Properties of Integer Exponents to generate equivalent expressions to (4^3 ⋅ 7^-2)^-5/7^9 ⋅ 4^-13 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
Answered by
Stranger danger
thats wrong
Answered by
Stranger danger
Apply the Properties of Integer Exponents to generate equivalent expressions to 2^2/2^−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.
Answered by
Stranger danger
Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 ⋅ 5^−2/(−2)^−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
Answered by
Stranger danger
wrong
Answered by
Stranger danger
wrong again
Answered by
Stranger danger
Apply the Properties of Integer Exponents to generate equivalent expressions to (4^3 ⋅ 7^-2)^-5/7^9 ⋅ 4^-13 with only positive exponents, then solve the expression Your answer will be a simplified fraction with no remaining exponents
(4^3 ⋅ 7^-2)^-5/7^9 ⋅ 4^-13 = ??????
(4^3 ⋅ 7^-2)^-5/7^9 ⋅ 4^-13 = ??????
Answered by
Stranger danger
ples try again
Answered by
Stranger danger
its still wrong!
Answered by
Stranger danger
BOT OMG
Answered by
GPT 3.5
$(4^3 \cdot 7^{-2})^{-5}/7^9$ means the following:
First, we calculate the value inside the parentheses: $4^3 \cdot 7^{-2}$.
$4^3$ is equal to $4 \times 4 \times 4 = 64$, and $7^{-2}$ is equal to $\frac{1}{7^2} = \frac{1}{49}$.
So, $4^3 \cdot 7^{-2}$ equals $64 \cdot \frac{1}{49} = \frac{64}{49}$.
Next, we raise this result to the power of $-5$, which means we take the reciprocal and raise it to the power of $5$.
So, $\left(\frac{64}{49}\right)^{-5}$ equals $\left(\frac{49}{64}\right)^5 = \frac{49^5}{64^5}$.
Finally, we divide this by $7^9$.
So, $\frac{\left(\frac{49^5}{64^5}\right)}{7^9} = \frac{49^5}{64^5 \cdot 7^9}$.
Therefore, the expression $(4^3 \cdot 7^{-2})^{-5}/7^9$ simplifies to $\frac{49^5}{64^5 \cdot 7^9}$.
First, we calculate the value inside the parentheses: $4^3 \cdot 7^{-2}$.
$4^3$ is equal to $4 \times 4 \times 4 = 64$, and $7^{-2}$ is equal to $\frac{1}{7^2} = \frac{1}{49}$.
So, $4^3 \cdot 7^{-2}$ equals $64 \cdot \frac{1}{49} = \frac{64}{49}$.
Next, we raise this result to the power of $-5$, which means we take the reciprocal and raise it to the power of $5$.
So, $\left(\frac{64}{49}\right)^{-5}$ equals $\left(\frac{49}{64}\right)^5 = \frac{49^5}{64^5}$.
Finally, we divide this by $7^9$.
So, $\frac{\left(\frac{49^5}{64^5}\right)}{7^9} = \frac{49^5}{64^5 \cdot 7^9}$.
Therefore, the expression $(4^3 \cdot 7^{-2})^{-5}/7^9$ simplifies to $\frac{49^5}{64^5 \cdot 7^9}$.
Answered by
GPT 3.5
To simplify the expression and convert all exponents to positive, we can apply the properties of integer exponents:
$(4^3 \cdot 7^{-2})^{-5}/7^9 \cdot 4^{-13}$
First, let's simplify the expression inside the parentheses:
$4^3 = 4 \cdot 4 \cdot 4 = 64$
$7^{-2} = \frac{1}{7^2} = \frac{1}{49}$
Now substitute the values back into the expression:
$(64 \cdot \frac{1}{49})^{-5}/7^9 \cdot 4^{-13}$
Next, let's simplify the expression further by applying the exponent rules:
$(\frac{64}{49})^{-5}/7^9 \cdot 4^{-13}$
To simplify the fraction in the numerator, we invert the fraction and change the sign of the exponent:
$(\frac{49}{64})^{5}/7^9 \cdot 4^{-13}$
Since $4^{-13}$ is in the denominator, we can rewrite it as $\frac{1}{4^{13}}$:
$(\frac{49}{64})^{5}/7^9 \cdot \frac{1}{4^{13}}$
Now, rearrange the terms to separate the numerator and denominator:
$\frac{(\frac{49}{64})^5}{7^9 \cdot 4^{13}}$
To simplify further, we can evaluate each part separately:
$49^5 = 49 \cdot 49 \cdot 49 \cdot 49 \cdot 49 = 5764801$
$64^5 = 64 \cdot 64 \cdot 64 \cdot 64 \cdot 64 = 1073741824$
$7^9 = 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 = 40353607$
$4^{13} = 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 = 67108864$
Substituting these values back into the expression:
$\frac{5764801}{40353607 \cdot 1073741824 \cdot 67108864}$
Now, let's simplify the numerator and denominator:
$\frac{5764801}{288441413567866689781422848}$
This fraction cannot be simplified any further, so the final answer is:
$\frac{5764801}{288441413567866689781422848}$
$(4^3 \cdot 7^{-2})^{-5}/7^9 \cdot 4^{-13}$
First, let's simplify the expression inside the parentheses:
$4^3 = 4 \cdot 4 \cdot 4 = 64$
$7^{-2} = \frac{1}{7^2} = \frac{1}{49}$
Now substitute the values back into the expression:
$(64 \cdot \frac{1}{49})^{-5}/7^9 \cdot 4^{-13}$
Next, let's simplify the expression further by applying the exponent rules:
$(\frac{64}{49})^{-5}/7^9 \cdot 4^{-13}$
To simplify the fraction in the numerator, we invert the fraction and change the sign of the exponent:
$(\frac{49}{64})^{5}/7^9 \cdot 4^{-13}$
Since $4^{-13}$ is in the denominator, we can rewrite it as $\frac{1}{4^{13}}$:
$(\frac{49}{64})^{5}/7^9 \cdot \frac{1}{4^{13}}$
Now, rearrange the terms to separate the numerator and denominator:
$\frac{(\frac{49}{64})^5}{7^9 \cdot 4^{13}}$
To simplify further, we can evaluate each part separately:
$49^5 = 49 \cdot 49 \cdot 49 \cdot 49 \cdot 49 = 5764801$
$64^5 = 64 \cdot 64 \cdot 64 \cdot 64 \cdot 64 = 1073741824$
$7^9 = 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 = 40353607$
$4^{13} = 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 = 67108864$
Substituting these values back into the expression:
$\frac{5764801}{40353607 \cdot 1073741824 \cdot 67108864}$
Now, let's simplify the numerator and denominator:
$\frac{5764801}{288441413567866689781422848}$
This fraction cannot be simplified any further, so the final answer is:
$\frac{5764801}{288441413567866689781422848}$
Answered by
GPT 3.5
To apply the properties of integer exponents and simplify the expression, we can start by evaluating the part inside the parentheses:
$(4^3 \cdot 7^{-2})^{-5}/7^9 \cdot 4^{-13}$
$4^3 = 4 \cdot 4 \cdot 4 = 64$
$7^{-2} = \frac{1}{7^2} = \frac{1}{49}$
Hence, the expression now becomes:
$(64 \cdot \frac{1}{49})^{-5}/7^9 \cdot 4^{-13}$
Next, let's simplify the numerator by applying the exponent rule for the power of a product:
$(\frac{64}{49})^{-5}/7^9 \cdot 4^{-13}$
To simplify the fractional exponent, we can flip the fraction and change the sign of the exponent:
$(\frac{49}{64})^5/7^9 \cdot 4^{-13}$
Since we want to convert all exponents to positive, we can express $4^{-13}$ as $\frac{1}{4^{13}}$:
$(\frac{49}{64})^5/7^9 \cdot \frac{1}{4^{13}}$
Now, rearranging the terms to separate the numerator and denominator, we get:
$\frac{(\frac{49}{64})^5}{7^9 \cdot 4^{13}}$
To simplify further, let's evaluate each part separately:
$49^5 = 49 \cdot 49 \cdot 49 \cdot 49 \cdot 49 = 5764801$
$64^5 = 64 \cdot 64 \cdot 64 \cdot 64 \cdot 64 = 1073741824$
$7^9 = 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 = 40353607$
$4^{13} = 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 = 67108864$
Substituting these values back into the expression:
$\frac{5764801}{40353607 \cdot 1073741824 \cdot 67108864}$
Now, let's simplify the fraction:
$\frac{5764801}{288441413567866689781422848}$
Hence, the final answer as a simplified fraction with no remaining exponents is:
$\frac{5764801}{288441413567866689781422848}$
$(4^3 \cdot 7^{-2})^{-5}/7^9 \cdot 4^{-13}$
$4^3 = 4 \cdot 4 \cdot 4 = 64$
$7^{-2} = \frac{1}{7^2} = \frac{1}{49}$
Hence, the expression now becomes:
$(64 \cdot \frac{1}{49})^{-5}/7^9 \cdot 4^{-13}$
Next, let's simplify the numerator by applying the exponent rule for the power of a product:
$(\frac{64}{49})^{-5}/7^9 \cdot 4^{-13}$
To simplify the fractional exponent, we can flip the fraction and change the sign of the exponent:
$(\frac{49}{64})^5/7^9 \cdot 4^{-13}$
Since we want to convert all exponents to positive, we can express $4^{-13}$ as $\frac{1}{4^{13}}$:
$(\frac{49}{64})^5/7^9 \cdot \frac{1}{4^{13}}$
Now, rearranging the terms to separate the numerator and denominator, we get:
$\frac{(\frac{49}{64})^5}{7^9 \cdot 4^{13}}$
To simplify further, let's evaluate each part separately:
$49^5 = 49 \cdot 49 \cdot 49 \cdot 49 \cdot 49 = 5764801$
$64^5 = 64 \cdot 64 \cdot 64 \cdot 64 \cdot 64 = 1073741824$
$7^9 = 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 = 40353607$
$4^{13} = 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 = 67108864$
Substituting these values back into the expression:
$\frac{5764801}{40353607 \cdot 1073741824 \cdot 67108864}$
Now, let's simplify the fraction:
$\frac{5764801}{288441413567866689781422848}$
Hence, the final answer as a simplified fraction with no remaining exponents is:
$\frac{5764801}{288441413567866689781422848}$
Answered by
GPT 3.5
Apologies for the mistake. Let's go through the simplification process again correctly:
To simplify the expression and convert all exponents to positive, we can apply the properties of integer exponents:
$(4^3 \cdot 7^{-2})^{-5}/7^9 \cdot 4^{-13}$
First, let's simplify the expression inside the parentheses:
$4^3 = 4 \cdot 4 \cdot 4 = 64$
$7^{-2} = \frac{1}{7^2} = \frac{1}{49}$
Now substitute the values back into the expression:
$(64 \cdot \frac{1}{49})^{-5}/7^9 \cdot 4^{-13}$
Next, let's simplify the expression further by applying the exponent rules:
$(\frac{64}{49})^{-5}/7^9 \cdot 4^{-13}$
To simplify the fraction in the numerator, we invert the fraction and change the sign of the exponent:
$(\frac{49}{64})^{5}/7^9 \cdot 4^{-13}$
Since $4^{-13}$ is in the denominator, we can rewrite it as $\frac{1}{4^{13}}$:
$(\frac{49}{64})^{5}/7^9 \cdot \frac{1}{4^{13}}$
Now, rearrange the terms to separate the numerator and denominator:
$\frac{(\frac{49}{64})^5}{7^9 \cdot 4^{13}}$
To simplify further, we can evaluate each part separately:
$49^5 = 49 \cdot 49 \cdot 49 \cdot 49 \cdot 49 = 5764801$
$64^5 = 64 \cdot 64 \cdot 64 \cdot 64 \cdot 64 = 1073741824$
$7^9 = 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 = 40353607$
$4^{13} = 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 = 67108864$
Substituting these values back into the expression:
$\frac{5764801}{40353607 \cdot 1073741824 \cdot 67108864}$
Now, let's simplify the numerator and denominator:
$\frac{5764801}{288441413567866689781422848}$
This fraction cannot be simplified any further, so the simplified expression is:
$\frac{5764801}{288441413567866689781422848}$
To simplify the expression and convert all exponents to positive, we can apply the properties of integer exponents:
$(4^3 \cdot 7^{-2})^{-5}/7^9 \cdot 4^{-13}$
First, let's simplify the expression inside the parentheses:
$4^3 = 4 \cdot 4 \cdot 4 = 64$
$7^{-2} = \frac{1}{7^2} = \frac{1}{49}$
Now substitute the values back into the expression:
$(64 \cdot \frac{1}{49})^{-5}/7^9 \cdot 4^{-13}$
Next, let's simplify the expression further by applying the exponent rules:
$(\frac{64}{49})^{-5}/7^9 \cdot 4^{-13}$
To simplify the fraction in the numerator, we invert the fraction and change the sign of the exponent:
$(\frac{49}{64})^{5}/7^9 \cdot 4^{-13}$
Since $4^{-13}$ is in the denominator, we can rewrite it as $\frac{1}{4^{13}}$:
$(\frac{49}{64})^{5}/7^9 \cdot \frac{1}{4^{13}}$
Now, rearrange the terms to separate the numerator and denominator:
$\frac{(\frac{49}{64})^5}{7^9 \cdot 4^{13}}$
To simplify further, we can evaluate each part separately:
$49^5 = 49 \cdot 49 \cdot 49 \cdot 49 \cdot 49 = 5764801$
$64^5 = 64 \cdot 64 \cdot 64 \cdot 64 \cdot 64 = 1073741824$
$7^9 = 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 = 40353607$
$4^{13} = 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 = 67108864$
Substituting these values back into the expression:
$\frac{5764801}{40353607 \cdot 1073741824 \cdot 67108864}$
Now, let's simplify the numerator and denominator:
$\frac{5764801}{288441413567866689781422848}$
This fraction cannot be simplified any further, so the simplified expression is:
$\frac{5764801}{288441413567866689781422848}$
Answered by
GPT 3.5
To apply the properties of integer exponents and simplify the expression, we can start by writing the expression with positive exponents:
2^2 / 2^(-4)
The property of division with the same base tells us that when we divide two numbers with the same base, we subtract their exponents:
2^(2 - (-4))
Simplifying the exponent subtraction:
2^6
Therefore, the expression 2^2 / 2^(-4) is equivalent to 2^6.
To evaluate 2^6, we multiply 2 by itself six times:
2 * 2 * 2 * 2 * 2 * 2 = 64
Hence, the solution to the expression 2^2 / 2^(-4) is 64 as a whole number.
2^2 / 2^(-4)
The property of division with the same base tells us that when we divide two numbers with the same base, we subtract their exponents:
2^(2 - (-4))
Simplifying the exponent subtraction:
2^6
Therefore, the expression 2^2 / 2^(-4) is equivalent to 2^6.
To evaluate 2^6, we multiply 2 by itself six times:
2 * 2 * 2 * 2 * 2 * 2 = 64
Hence, the solution to the expression 2^2 / 2^(-4) is 64 as a whole number.
Answered by
GPT 3.5
To apply the properties of integer exponents and simplify the expression, let's break it down in steps:
Step 1: Simplify each base with an exponent of zero or a negative exponent:
4^0 = 1 (Any nonzero number to the power of 0 is equal to 1.)
5^(-2) = 1/5^2 = 1/25 (A negative exponent indicates taking the reciprocal of the number raised to the positive exponent.)
(-2)^(-3) = (1/(-2))^3 = (1/(-2))^3 = -8 (A negative base raised to an odd exponent gives a negative result.)
After simplifying these bases, the expression becomes:
1 ⋅ 1/25 / -8
Step 2: Simplify the division:
1 ⋅ 1/25 / -8 = (1/25) / -8
Since dividing by a number is the same as multiplying by its reciprocal, we can express this as:
(1/25) * (-1/8)
Step 3: Multiply the fractions:
(1/25) * (-1/8) = -1/200
Therefore, the simplified expression for 4^0 ⋅ 5^−2/(−2)^−3 is -1/200.
Step 1: Simplify each base with an exponent of zero or a negative exponent:
4^0 = 1 (Any nonzero number to the power of 0 is equal to 1.)
5^(-2) = 1/5^2 = 1/25 (A negative exponent indicates taking the reciprocal of the number raised to the positive exponent.)
(-2)^(-3) = (1/(-2))^3 = (1/(-2))^3 = -8 (A negative base raised to an odd exponent gives a negative result.)
After simplifying these bases, the expression becomes:
1 ⋅ 1/25 / -8
Step 2: Simplify the division:
1 ⋅ 1/25 / -8 = (1/25) / -8
Since dividing by a number is the same as multiplying by its reciprocal, we can express this as:
(1/25) * (-1/8)
Step 3: Multiply the fractions:
(1/25) * (-1/8) = -1/200
Therefore, the simplified expression for 4^0 ⋅ 5^−2/(−2)^−3 is -1/200.
Answered by
GPT 3.5
Apologies for the mistake. Let's go through the simplification process again correctly:
To apply the properties of integer exponents and simplify the expression, let's break it down in steps:
Step 1: Simplify each base with an exponent of zero or a negative exponent:
4^0 = 1 (Any nonzero number to the power of 0 is equal to 1.)
5^(-2) = 1/5^2 = 1/25 (A negative exponent indicates taking the reciprocal of the number raised to the positive exponent.)
(-2)^(-3) = (1/(-2))^3 = (-1/2)^3 = -1/8 (A negative base raised to an odd exponent gives a negative result.)
After simplifying these bases, the expression becomes:
1 ⋅ 1/25 / -1/8
Step 2: Simplify the division:
1 ⋅ 1/25 / -1/8 = (1⋅8) / (25⋅-1)
Simplifying the numerator and denominator:
8 / -25
Therefore, the simplified expression for 4^0 ⋅ 5^−2 / (−2)^−3 is 8 / -25.
To apply the properties of integer exponents and simplify the expression, let's break it down in steps:
Step 1: Simplify each base with an exponent of zero or a negative exponent:
4^0 = 1 (Any nonzero number to the power of 0 is equal to 1.)
5^(-2) = 1/5^2 = 1/25 (A negative exponent indicates taking the reciprocal of the number raised to the positive exponent.)
(-2)^(-3) = (1/(-2))^3 = (-1/2)^3 = -1/8 (A negative base raised to an odd exponent gives a negative result.)
After simplifying these bases, the expression becomes:
1 ⋅ 1/25 / -1/8
Step 2: Simplify the division:
1 ⋅ 1/25 / -1/8 = (1⋅8) / (25⋅-1)
Simplifying the numerator and denominator:
8 / -25
Therefore, the simplified expression for 4^0 ⋅ 5^−2 / (−2)^−3 is 8 / -25.
Answered by
GPT 3.5
Apologies once again for the mistake. Let's go through the simplification process correctly this time:
To apply the properties of integer exponents and simplify the expression, let's break it down step by step:
Step 1: Simplify each base with an exponent of zero or a negative exponent:
4^0 = 1 (Any non-zero number raised to the power of 0 is equal to 1.)
5^(-2) = 1/(5^2) = 1/25 (Negative exponent indicates taking the reciprocal of the number raised to the positive exponent.)
(-2)^(-3) = 1/((-2)^3) = 1/(-8) = -1/8 (Negative exponent indicates taking the reciprocal of the number raised to the positive exponent.)
After simplifying these bases, the expression becomes:
1 ⋅ 1/25 / -1/8
Step 2: Simplify the division:
1 ⋅ 1/25 / -1/8 = (1 ⋅ 1/25) ⋅ (-8/1)
Simplifying the numerator and denominator separately:
1 ⋅ 1/25 = 1/25
Now, we have:
1/25 ⋅ -8/1
Step 3: Multiply the fractions:
1/25 ⋅ -8/1 = (-8/25)
Therefore, the simplified expression for 4^0 ⋅ 5^(-2) / (-2)^(-3) is -8/25.
To apply the properties of integer exponents and simplify the expression, let's break it down step by step:
Step 1: Simplify each base with an exponent of zero or a negative exponent:
4^0 = 1 (Any non-zero number raised to the power of 0 is equal to 1.)
5^(-2) = 1/(5^2) = 1/25 (Negative exponent indicates taking the reciprocal of the number raised to the positive exponent.)
(-2)^(-3) = 1/((-2)^3) = 1/(-8) = -1/8 (Negative exponent indicates taking the reciprocal of the number raised to the positive exponent.)
After simplifying these bases, the expression becomes:
1 ⋅ 1/25 / -1/8
Step 2: Simplify the division:
1 ⋅ 1/25 / -1/8 = (1 ⋅ 1/25) ⋅ (-8/1)
Simplifying the numerator and denominator separately:
1 ⋅ 1/25 = 1/25
Now, we have:
1/25 ⋅ -8/1
Step 3: Multiply the fractions:
1/25 ⋅ -8/1 = (-8/25)
Therefore, the simplified expression for 4^0 ⋅ 5^(-2) / (-2)^(-3) is -8/25.
Answered by
GPT 3.5
Let's break down the expression step by step:
(4^3 ⋅ 7^-2)^-5 / 7^9 ⋅ 4^-13
First, let's simplify the expression inside the parentheses:
4^3 = 4 * 4 * 4 = 64
7^-2 = 1 / 7^2 = 1 / 49
So, (4^3 ⋅ 7^-2) becomes (64 ⋅ 1/49) = 64/49.
Next, let's substitute this result back into the expression:
(64/49)^-5 / 7^9 ⋅ 4^-13
To eliminate negative exponents, we can apply the property of taking the reciprocal of a base raised to a negative exponent:
(49/64)^5 / 7^9 ⋅ (1/4)^13
Now, let's further simplify:
(49^5 / 64^5) / 7^9 ⋅ 1/4^13
Next, let's evaluate each part separately:
49^5 = 49 * 49 * 49 * 49 * 49 = 5764801
64^5 = 64 * 64 * 64 * 64 * 64 = 1073741824
7^9 = 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 = 40353607
4^13 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 67108864
Now, substitute these values back into the expression:
(5764801 / 1073741824) / 40353607 ⋅ 1 / 67108864
To simplify the expression further, we can multiply the numerators and multiply the denominators:
(5764801 / 1073741824) * (1 / 40353607) * (1 / 67108864)
Now, multiply the numerators together and multiply the denominators together:
5764801 / (1073741824 * 40353607 * 67108864)
Simplifying the denominator:
5764801 / 288441413567866689781422848
Thus, the simplified fraction, without any remaining exponents, is:
5764801 / 288441413567866689781422848.
(4^3 ⋅ 7^-2)^-5 / 7^9 ⋅ 4^-13
First, let's simplify the expression inside the parentheses:
4^3 = 4 * 4 * 4 = 64
7^-2 = 1 / 7^2 = 1 / 49
So, (4^3 ⋅ 7^-2) becomes (64 ⋅ 1/49) = 64/49.
Next, let's substitute this result back into the expression:
(64/49)^-5 / 7^9 ⋅ 4^-13
To eliminate negative exponents, we can apply the property of taking the reciprocal of a base raised to a negative exponent:
(49/64)^5 / 7^9 ⋅ (1/4)^13
Now, let's further simplify:
(49^5 / 64^5) / 7^9 ⋅ 1/4^13
Next, let's evaluate each part separately:
49^5 = 49 * 49 * 49 * 49 * 49 = 5764801
64^5 = 64 * 64 * 64 * 64 * 64 = 1073741824
7^9 = 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 = 40353607
4^13 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 67108864
Now, substitute these values back into the expression:
(5764801 / 1073741824) / 40353607 ⋅ 1 / 67108864
To simplify the expression further, we can multiply the numerators and multiply the denominators:
(5764801 / 1073741824) * (1 / 40353607) * (1 / 67108864)
Now, multiply the numerators together and multiply the denominators together:
5764801 / (1073741824 * 40353607 * 67108864)
Simplifying the denominator:
5764801 / 288441413567866689781422848
Thus, the simplified fraction, without any remaining exponents, is:
5764801 / 288441413567866689781422848.
Answered by
GPT 3.5
Apologies for the confusion. Let's simplify the expression step by step:
(4^3 ⋅ 7^-2)^-5 / 7^9 ⋅ 4^-13
First, let's simplify the expression inside the parentheses:
4^3 = 4 * 4 * 4 = 64
7^-2 = 1 / 7^2 = 1/49
So, (
(4^3 ⋅ 7^-2)^-5 / 7^9 ⋅ 4^-13
First, let's simplify the expression inside the parentheses:
4^3 = 4 * 4 * 4 = 64
7^-2 = 1 / 7^2 = 1/49
So, (