Simplify the expression. $$\frac { \left( 8 ^ { - 2 } z ^ { - 5 } y \right) ^ { - 1 } } { \left( 5 y ^ { 5 } z ^ { - 1 } \right) ^ { 3 } \left( 5 y z ^ { - 1 } \right) ^ { - 2 } }$$
Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.
A) $\quad \frac { 64 z ^ { 6 } } { 5 y ^ { 14 } }$
B) $\frac { 5 y ^ { 14 } } { 64 z ^ { 6 } }$
C) $\quad \frac { 64 z ^ { 14 } } { 5 y ^ { 6 } }$
D) $\frac { 8 z ^ { 5 } } { 5 y ^ { 15 } }$

Question

Quizplus · Accepted Answer

First, simplify the expression by applying the laws of exponents. The given expression is $\frac { \left( 8 ^ { - 2 } z ^ { - 5 } y \right) ^ { - 1 } } { \left( 5 y ^ { 5 } z ^ { - 1 } \right) ^ { 3 } \left( 5 y z ^ { - 1 } \right) ^ { - 2 } }$. When simplifying, invert the numerator and change the signs of its exponents to get $8^2z^5y^{-1}$. For the denominator, distribute the exponents to get $5^3y^{15}z^{-3}\cdot5^{-2}y^{-2}z^2$. Simplify further to get $\frac{64z^5}{y}\cdot\frac{1}{125y^{15}/25z}$, which simplifies to $\frac{64z^6}{5y^{14}}$, matching choice A.

Simplify the Expression Write the Answer Without Using Negative Exponents 64z65y14\quad \frac { 64 z ^ { 6 } } { 5 y ^ { 14 } }5y1464z6​

Simplify the Expression Write the Answer Without Using Negative Exponents $\quad \frac { 64 z ^ { 6 } } { 5 y ^ { 14 } }$