$(4^3 \cdot 7^{-2})^{-5}/7^9$ 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 $\frac{49^5}{64^5 \cdot 7^9}$.
bot what does $(4^3 \cdot 7^{-2})^{-5}/7^9 \cdot mean?
21 answers
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.
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:
$\frac{5764801}{288441413567866689781422848}$
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.
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:
$\frac{5764801}{288441413567866689781422848}$
thats wrong
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:
$\frac{5764801}{288441413567866689781422848}$
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.
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.
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.
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.
wrong
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.
wrong again
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.
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 = ??????
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.
ples try again
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, (
its still wrong!
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1 answer