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Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)^0 with only positive exponents, th...Asked by Treetard
Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3 x 27^-7)^0/3^4 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
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Answered by
Treetard
that’s wrong it has to be a simplified fraction
Answered by
Treetard
it has to be a fraction so you’re wrong
Answered by
Treetard
it NEEDS to be a fraction so you’re wrong again.
Answered by
Treetard
you’re still wrong
Answered by
Treetard
your entire answer is wrong
Answered by
Treetard
Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3 x 27^7)^0/3^4 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
Answer
Apply the Properties of Integer Exponents to generate equivalent expressions to (43 ⋅ 7−2)−579 ⋅ 4−13 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(4^3 ⋅ 7^−2)^−5 / 7^9 ⋅ 4^−13=
(4^3 ⋅ 7^−2)^−5 / 7^9 ⋅ 4^−13=
Answered by
GPT 3.5
To apply the properties of integer exponents, we can use the following rules:
1. Product of powers property: (a^m)(a^n) = a^(m+n)
2. Power of a power property: (a^m)^n = a^(m*n)
3. Quotient of powers property: a^m/a^n = a^(m-n)
4. Negative exponent rule: a^-n = 1/a^n
Let's simplify the expression step by step:
(14^3 x 27^-7)^(0/3^4)
First, we can simplify the exponents using the power of a power property:
(14^(3*(0/3^4)) x (27^(-7*(0/3^4)))
Anything raised to the power of zero is equal to 1, so we have:
(14^0 x 27^0)
Next, we can simplify the exponents further:
(1 x 1)
Multiplying 1 by any number does not change the value, so our simplified expression is:
1.
Therefore, the solution to the expression is 1.
1. Product of powers property: (a^m)(a^n) = a^(m+n)
2. Power of a power property: (a^m)^n = a^(m*n)
3. Quotient of powers property: a^m/a^n = a^(m-n)
4. Negative exponent rule: a^-n = 1/a^n
Let's simplify the expression step by step:
(14^3 x 27^-7)^(0/3^4)
First, we can simplify the exponents using the power of a power property:
(14^(3*(0/3^4)) x (27^(-7*(0/3^4)))
Anything raised to the power of zero is equal to 1, so we have:
(14^0 x 27^0)
Next, we can simplify the exponents further:
(1 x 1)
Multiplying 1 by any number does not change the value, so our simplified expression is:
1.
Therefore, the solution to the expression is 1.
Answered by
GPT 3.5
Apologies for the mistake. Let's apply the properties of integer exponents to generate equivalent expressions with positive exponents:
(14^3 x 27^-7)^(0/3^4)
Using the negative exponent rule, we can rewrite 27^-7 as 1/27^7:
(14^3 x (1/27^7))^(0/3^4)
Next, we can simplify the exponents:
(14^3 x 1/27^7)^0
In any expression raised to the power of 0, the result is always 1:
1^0
Therefore, the solution to the expression is 1.
(14^3 x 27^-7)^(0/3^4)
Using the negative exponent rule, we can rewrite 27^-7 as 1/27^7:
(14^3 x (1/27^7))^(0/3^4)
Next, we can simplify the exponents:
(14^3 x 1/27^7)^0
In any expression raised to the power of 0, the result is always 1:
1^0
Therefore, the solution to the expression is 1.
Answered by
GPT 3.5
Apologies for the confusion earlier. Let's try again:
To simplify the expression (14^3 x 27^-7)^(0/3^4) and generate equivalent expressions with positive exponents, we can apply the rules of integer exponents:
First, let's simplify the exponents inside the parentheses:
14^3 x (27^-7)^(0/3^4)
The property of a power to a power tells us that (27^-7)^(0/3^4) is equivalent to 27^((-7)*(0/3^4)).
In this case, any term raised to the power of zero is equal to 1. Therefore, 27^0 = 1.
So, we are left with:
14^3 x 1
Using the product of powers property, we can simplify further:
14^3 = 2^3 x 7^3 = 8 x 343 = 2744
Thus, the expression simplifies to 2744.
To simplify the expression (14^3 x 27^-7)^(0/3^4) and generate equivalent expressions with positive exponents, we can apply the rules of integer exponents:
First, let's simplify the exponents inside the parentheses:
14^3 x (27^-7)^(0/3^4)
The property of a power to a power tells us that (27^-7)^(0/3^4) is equivalent to 27^((-7)*(0/3^4)).
In this case, any term raised to the power of zero is equal to 1. Therefore, 27^0 = 1.
So, we are left with:
14^3 x 1
Using the product of powers property, we can simplify further:
14^3 = 2^3 x 7^3 = 8 x 343 = 2744
Thus, the expression simplifies to 2744.
Answered by
GPT 3.5
Apologies for the repeated mistakes. Let's try again to simplify the expression and provide the answer as a simplified fraction:
To simplify (14^3 x 27^-7)^(0/3^4) with positive exponents, let's break it down step by step:
Step 1: Simplify the exponents inside the parentheses.
14^3 x (27^-7)^(0/3^4)
Recall that any number raised to the power of 0 is equal to 1. Therefore, (27^-7)^(0/3^4) simplifies to 1.
Step 2: Simplify the expression.
14^3 x 1
Step 3: Evaluate 14^3.
14^3 = 14 x 14 x 14 = 2744
Therefore, the simplified expression is 2744. As a simplified fraction, it can be written as 2744/1.
To simplify (14^3 x 27^-7)^(0/3^4) with positive exponents, let's break it down step by step:
Step 1: Simplify the exponents inside the parentheses.
14^3 x (27^-7)^(0/3^4)
Recall that any number raised to the power of 0 is equal to 1. Therefore, (27^-7)^(0/3^4) simplifies to 1.
Step 2: Simplify the expression.
14^3 x 1
Step 3: Evaluate 14^3.
14^3 = 14 x 14 x 14 = 2744
Therefore, the simplified expression is 2744. As a simplified fraction, it can be written as 2744/1.
Answered by
GPT 3.5
I apologize for the repeated errors. Let's try again to simplify the expression and provide the answer as a simplified fraction:
To simplify (14^3 x 27^-7)^(0/3^4) with positive exponents, we can break it down step by step:
Step 1: Simplify the exponents inside the parentheses.
(14^3 x 1/27^7)^(0/3^4)
Step 2: Simplify the expression.
To simplify 14^3, we have 14 x 14 x 14 = 2744.
To simplify 1/27^7, we can rewrite it as 27^-7, which means taking the reciprocal. So, 1/27^7 becomes 1/(1/27^7) = 27^7.
Therefore, we have (2744 x 27^7)^(0/3^4).
Step 3: Simplify the exponent.
Since any number raised to the power of 0 is equal to 1, the expression becomes 2744 x 27^7^0.
Step 4: Evaluate the remaining part.
Since 27^7^0 = 27^0 = 1, the expression simplifies to 2744 x 1 = 2744.
Hence, the simplified fraction is 2744/1.
To simplify (14^3 x 27^-7)^(0/3^4) with positive exponents, we can break it down step by step:
Step 1: Simplify the exponents inside the parentheses.
(14^3 x 1/27^7)^(0/3^4)
Step 2: Simplify the expression.
To simplify 14^3, we have 14 x 14 x 14 = 2744.
To simplify 1/27^7, we can rewrite it as 27^-7, which means taking the reciprocal. So, 1/27^7 becomes 1/(1/27^7) = 27^7.
Therefore, we have (2744 x 27^7)^(0/3^4).
Step 3: Simplify the exponent.
Since any number raised to the power of 0 is equal to 1, the expression becomes 2744 x 27^7^0.
Step 4: Evaluate the remaining part.
Since 27^7^0 = 27^0 = 1, the expression simplifies to 2744 x 1 = 2744.
Hence, the simplified fraction is 2744/1.
Answered by
GPT 3.5
Apologies once again for the previous incorrect responses. Let's proceed with the correct simplification of the expression.
We have: (14^3 x 27^-7)^(0/3^4)
First, let's simplify the exponents inside the parentheses:
14^3 x (1/27^7)^(0/3^4)
Next, we apply the property of a power to a power. For (1/27^7)^(0/3^4), the exponent 0 can be applied to the numerator and denominator separately:
14^3 x (1^0 / 27^(7*(0/3^4)))
Since any number to the power of 0 is equal to 1, we have:
14^3 x (1 / 27^(0/3^4))
Next, we simplify the exponent of 27 in the denominator:
14^3 x (1 / 27^(0/81))
Since any non-zero number to the power of 0 is equal to 1, the expression becomes:
14^3 x (1 / 27^0)
Now, we simplify the exponent of 27 in the denominator:
14^3 x (1 / 1)
Since any number divided by 1 is equal to itself, we have:
14^3
Evaluating 14^3:
14^3 = 14 x 14 x 14 = 2744
Therefore, the simplified expression is 2744, which can be written as the fraction 2744/1.
We have: (14^3 x 27^-7)^(0/3^4)
First, let's simplify the exponents inside the parentheses:
14^3 x (1/27^7)^(0/3^4)
Next, we apply the property of a power to a power. For (1/27^7)^(0/3^4), the exponent 0 can be applied to the numerator and denominator separately:
14^3 x (1^0 / 27^(7*(0/3^4)))
Since any number to the power of 0 is equal to 1, we have:
14^3 x (1 / 27^(0/3^4))
Next, we simplify the exponent of 27 in the denominator:
14^3 x (1 / 27^(0/81))
Since any non-zero number to the power of 0 is equal to 1, the expression becomes:
14^3 x (1 / 27^0)
Now, we simplify the exponent of 27 in the denominator:
14^3 x (1 / 1)
Since any number divided by 1 is equal to itself, we have:
14^3
Evaluating 14^3:
14^3 = 14 x 14 x 14 = 2744
Therefore, the simplified expression is 2744, which can be written as the fraction 2744/1.
Answered by
GPT 3.5
To generate equivalent expressions with positive exponents, we can apply the properties of integer exponents. Let's simplify (14^3 x 27^7)^0/3^4 step by step:
First, let's focus on the expression inside the parentheses: 14^3 x 27^7.
Using the product of powers property, we can combine the multiplication of these terms:
14^3 x 27^7 = (14 x 14 x 14) x (27 x 27 x 27 x 27 x 27 x 27 x 27)
Simplifying further:
14^3 x 27^7 = 2744 x 387,420,489
Next, let's simplify the denominator: 3^4 = 3 x 3 x 3 x 3 = 81.
Now, let's substitute these values back into the original expression:
(2744 x 387,420,489)^0 / 81
To simplify (2744 x 387,420,489)^0, we know that any non-zero number raised to the power of 0 is equal to 1. So, this term becomes 1.
Therefore, we now have 1 / 81 as our expression.
Simplifying further, we have:
1 / 81 = 1/81
So, the solution to the expression (14^3 x 27^7)^0 / 3^4, with positive exponents and simplified, is the fraction 1/81.
First, let's focus on the expression inside the parentheses: 14^3 x 27^7.
Using the product of powers property, we can combine the multiplication of these terms:
14^3 x 27^7 = (14 x 14 x 14) x (27 x 27 x 27 x 27 x 27 x 27 x 27)
Simplifying further:
14^3 x 27^7 = 2744 x 387,420,489
Next, let's simplify the denominator: 3^4 = 3 x 3 x 3 x 3 = 81.
Now, let's substitute these values back into the original expression:
(2744 x 387,420,489)^0 / 81
To simplify (2744 x 387,420,489)^0, we know that any non-zero number raised to the power of 0 is equal to 1. So, this term becomes 1.
Therefore, we now have 1 / 81 as our expression.
Simplifying further, we have:
1 / 81 = 1/81
So, the solution to the expression (14^3 x 27^7)^0 / 3^4, with positive exponents and simplified, is the fraction 1/81.
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