Question

Mario simplified the expression as shown.

Which statement explains Mario’s error?

Answer 1

The correct answer option is He should have also applied the exponent -3 to 4 to get
`4^(-3)z^(8 \cdot(-3)) = 4^(-3)z^(-24) = (1)/(64z^(24))`.

Explanation:

The following expression was to be simplified by Mario:

`(4z^8)^-3`

Given this expression, we need to apply this rule on it in order to simplify:

`(a b)^m = a^m \cdot b^m`

So we would get:

`(4z^8)^-3`

`4^(-3) \cdot (z^8)^(-3)`

`(1)/(4^3) \cdot z^(-24)`

`(1)/(64z^(24))`

This would be the right simplification for the given expression but by looking at Mario's work shown, we can conclude that:

He should have also applied the exponent -3 to 4 to get
`4^(-3)z^(8 \cdot(-3)) = 4^(-3)z^(-24) = (1)/(64z^(24))`.

Answer 2

Answer: Last option

Explanation:

1. According to the properties of exponents, you have that:

`a^(-n)=(1)/(a^n)\\\\(a^n)^m=a^(mn)`

2. Then, he must simplify the expression as following:

`(4z^8)^(-3)={4^(-3)z^(8(-3))=(1)/(64z^(24))`

3. Therefore, as you can see, should have also applied the negative exponent to 4 to get
`(4z^8)^(-3)={4^(-3)z^(8(-3))=(1)/(64z^(24))`