Simplify the expression and write the answer without negative exponents.
-$\frac { \left( 3 x y ^ { 4 } z ^ { - 2 } \right) ^ { 3 } } { \left( 4 x ^ { 6 } y z ^ { - 3 } \right) ^ { - 1 } }$
A) $- \frac { 27 y ^ { 13 } } { 4 x ^ { 3 } z ^ { 9 } }$
B) $\frac { 108 y ^ { 13 } } { x ^ { 5 } z ^ { 9 } }$
C) $- \frac { 27 x ^ { 9 } y ^ { 13 } } { 4 z ^ { 9 } }$
D) $\frac { 108 x ^ { 9 } y ^ { 13 } } { z ^ { 9 } }$

Question

Quizplus · Accepted Answer

First, apply the power rule to both the numerator and the denominator. In the numerator, each exponent is multiplied by 3, and in the denominator, the negative exponent means we take the reciprocal and multiply each exponent by -1. Simplifying gives us the expression in choice D.

Simplify the Expression and Write the Answer Without Negative Exponents (3xy4z−2)3(4x6yz−3)−1\frac { \left( 3 x y ^ { 4 } z ^ { - 2 } \right) ^ { 3 } } { \left( 4 x ^ { 6 } y z ^ { - 3 } \right) ^ { - 1 } }(4x6yz−3)−1(3xy4z−2)3​

Simplify the Expression and Write the Answer Without Negative Exponents $\frac { \left( 3 x y ^ { 4 } z ^ { - 2 } \right) ^ { 3 } } { \left( 4 x ^ { 6 } y z ^ { - 3 } \right) ^ { - 1 } }$