Question

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

Answer 1

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: