Simplify the expression. $$\left( \frac { 8 x ^ { - 4 } y ^ { 5 } z ^ { - 8 } } { 32 x ^ { 4 } y ^ { 12 } z ^ { - 13 } } \right) ^ { 3 }$$
Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.
A) $\quad \frac { z ^ { 5 } } { 4 x ^ { 8 } y ^ { 7 } }$
B) $\quad \frac { z ^ { 15 } } { 64 x ^ { 24 } y ^ { 21 } }$
C) $\quad \frac { z ^ { 15 } } { 64 x ^ { 21 } y ^ { 24 } }$
D) $\frac { z ^ { 15 } } { 64 x ^ { - 24 } y ^ { - 21 } }$
E) $\frac { z ^ { 5 } } { 4 x ^ { 24 } y ^ { 21 } }$

Question

Quizplus · Accepted Answer

First, simplify the expression inside the parentheses by dividing the numerators and denominators: $\frac{8}{32} = \frac{1}{4}$, $x^{-4 - 4} = x^{-8}$, $y^{5 - 12} = y^{-7}$, and $z^{-8 - (-13)} = z^{5}$. Then, apply the power of 3 to each component: $(\frac{1}{4})^3 = \frac{1}{64}$, $x^{-8 \cdot 3} = x^{-24}$, $y^{-7 \cdot 3} = y^{-21}$, and $z^{5 \cdot 3} = z^{15}$. The final expression is $\frac{z^{15}}{64x^{24}y^{21}}$, which matches choice B.

Simplify the Expression (8x−4y5z−832x4y12z−13)3\left( \frac { 8 x ^ { - 4 } y ^ { 5 } z ^ { - 8 } } { 32 x ^ { 4 } y ^ { 12 } z ^ { - 13 } } \right) ^ { 3 }(32x4y12z−138x−4y5z−8​)3

Simplify the Expression $\left( \frac { 8 x ^ { - 4 } y ^ { 5 } z ^ { - 8 } } { 32 x ^ { 4 } y ^ { 12 } z ^ { - 13 } } \right) ^ { 3 }$