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

Answer: Last option
Step-by-step explanation:
1. According to the properties of exponents, you have that:
[tex]a^{-n}=\frac{1}{a^n}\\\\(a^n)^m=a^{mn}[/tex]
2. Then, he must simplify the expression as following:
[tex](4z^8)^{-3}={4^{-3}z^{8(-3)}=\frac{1}{64z^{24}}[/tex]
3. Therefore, as you can see, should have also applied the negative exponent to 4 to get [tex](4z^8)^{-3}={4^{-3}z^{8(-3)}=\frac{1}{64z^{24}}[/tex]
Answer:
The correct answer option is He should have also applied the exponent -3 to 4 to get [tex]4^{-3}z^{8 \cdot(-3)} = 4^{-3}z^{-24} = \frac{1}{64z^{24}}[/tex].
Step-by-step explanation:
The following expression was to be simplified by Mario:
[tex] (4z^8)^-3 [/tex]
Given this expression, we need to apply this rule on it in order to simplify:
[tex] (a b)^m = a^m \cdot b^m [/tex]
So we would get:
[tex] (4z^8)^-3 [/tex]
[tex]4^{-3} \cdot (z^8)^{-3}[/tex]
[tex]\frac{1}{4^3} \cdot z^{-24}[/tex]
[tex]\frac{1}{64z^{24}}[/tex]
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 [tex]4^{-3}z^{8 \cdot(-3)} = 4^{-3}z^{-24} = \frac{1}{64z^{24}}[/tex].