Question

Mario simplified the expression as shown. Which statement explains Mario’s error?

Answer 1

Answer: Last option

Step-by-step explanation:

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

$a^{-n}=\frac{1}{a^n}\\\\(a^n)^m=a^{mn}$

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

$(4z^8)^{-3}={4^{-3}z^{8(-3)}=\frac{1}{64z^{24}}$

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

Answer 2

Answer:

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

Step-by-step 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:

$(4z^8)^-3$

$4^{-3} \cdot (z^8)^{-3}$

$\frac{1}{4^3} \cdot z^{-24}$

$\frac{1}{64z^{24}}$

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 $4^{-3}z^{8 \cdot(-3)} = 4^{-3}z^{-24} = \frac{1}{64z^{24}}$.