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Use the properties of exponents to rewrite this expression. What is the value of the rewritten expression when a= -5 ?

A. -250
B. -20
C. -60
D. -500

User Prc
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1 Answer

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This fraction is not one of the options provided in the multiple-choice answers. Therefore, none of the given options are correct

The image contains an expression that we need to simplify using the properties of exponents, and then evaluate for
\( a = -5 \). The expression is:


\[ \left( (2a^4)/(a^(0)a^6) \right)^2 \]

Let's simplify the expression step by step before substituting the value of
\( a \):

1. Simplify inside the parentheses:

-
\( a^(0) = 1 \) (Any non-zero number raised to the 0th power is 1).

-
\( 2a^4 \) divided by
\( a^6 \) is \( 2a^(4-6) \) due to the quotient rule of exponents
(\( a^m / a^n = a^(m-n) \)).

2. The expression inside the parentheses becomes
\( 2a^(-2) \).

3. Square the result:

-
\( (2a^(-2))^2 \) is
\( 2^2 \cdot a^(-2 \cdot 2) \) due to the power of a product rule
(\( (ab)^n = a^n \cdot b^n \)).

4. Calculate the squared terms:

-
\( 2^2 = 4 \)

-
\( a^(-2 \cdot 2) = a^(-4) \)

5. The simplified expression is
\( 4a^(-4) \).

Now let's substitute
\( a = -5 \) into the simplified expression:


\[ 4(-5)^(-4) \]

6. Calculate the exponent:

-
\( (-5)^(-4) \) is \( (1)/((-5)^4) \).

7. Calculate \( (-5)^4 \):

-
\( (-5)^4 = (-5) \cdot (-5) \cdot (-5) \cdot (-5) = 625 \).

8. So,
\( (1)/((-5)^4) \) becomes \( (1)/(625) \).

9. Multiply by 4:

-
\( 4 \cdot (1)/(625) = (4)/(625) \).

10. Simplify if possible:

- Since
\( (4)/(625) \) cannot be simplified further, this is the final result.

To find the numeric value:


\[ 4(-5)^(-4) = 4 \cdot (1)/(625) = (4)/(625) \]

This fraction is not one of the options provided in the multiple-choice answers.

the complete Question is given below:

Use the properties of exponents to rewrite this expression. What is the value of the-example-1
User Pazcal
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