Simplify the expression. $\frac { \left( 8 ^ { - 2 } z ^ { - 4 } y \right) ^ { - 1 } } { \left( 5 y ^ { 3 } z ^ { - 3 } \right) ^ { 4 } \left( 5 y z ^ { - 3 } \right) ^ { - 1 } }$ Write the answer without using negative exponents.Assume that all variables are restricted to those numbers for which the expression is defined.
A)$\frac{8 z^{12}}{125 y^{13}}$
B)$\frac{64 z^{12}}{125 y^{13}}$
C)$\frac{125 y^{12}}{64 z^{13}}$
D) $\quad \frac { 64 z ^ { 13 } } { 125 y ^ { 12 } }$

Question

Simplify the expression. $\frac { \left( 8 ^ { - 2 } z ^ { - 4 } y \right) ^ { - 1 } } { \left( 5 y ^ { 3 } z ^ { - 3 } \right) ^ { 4 } \left( 5 y z ^ { - 3 } \right) ^ { - 1 } }$ Write the answer without using negative exponents.Assume that all variables are restricted to those numbers for which the expression is defined. 
A)$\frac{8 z^{12}}{125 y^{13}}$
B)$\frac{64 z^{12}}{125 y^{13}}$
C)$\frac{125 y^{12}}{64 z^{13}}$
D) $\quad \frac { 64 z ^ { 13 } } { 125 y ^ { 12 } }$

Quizplus · Accepted Answer

To simplify the expression, we follow the order of operations (PEMDAS):

1. Simplify the term inside the parentheses of the numerator:

$\left( 8 ^ { - 2 } z ^ { - 4 } y \right) ^ { - 1 } = \frac{1}{8^{-2}z^{-4}y^{-1}} = \frac{8^2 z^4}{y}$

2. Simplify the terms inside the parentheses of the denominator:

$\left( 5 y ^ { 3 } z ^ { - 3 } \right) ^ { 4 } = 5^4 y^{12} z^{-12} = \frac{625y^{12}}{z^{12}}$

and

$\left( 5 y z ^ { - 3 } \right) ^ { - 1 } = \frac{1}{5yz^{-3}} = \frac{z^3}{5y}$

3. Substitute the simplified terms into the expression:

$\frac{\frac{8^2 z^4}{y}}{\frac{625y^{12}}{z^{12}}\cdot\frac{z^3}{5y}} = \frac{8^2z^4\cdot z^{12}\cdot5y}{y\cdot625y^{12}\cdot5z^3} = \frac{64z^{16}}{3125y^{13}} = \frac{64z^{13}}{125y^{13}}$

Therefore, the simplified expression is $\boxed{\textbf{(D)}\ \frac { 64 z ^ { 13 } } { 125 y ^ { 12 } }}$.

Simplify the Expression Write the Answer Without Using Negative Exponents 8z12125y13\frac{8 z^{12}}{125 y^{13}}125y138z12​

Simplify the Expression Write the Answer Without Using Negative Exponents $\frac{8 z^{12}}{125 y^{13}}$