Simplify: $\left( \frac { 81 y ^ { 8 } } { 16 } \right) ^ { - \frac { 3 } { 4 } }$
A) $\frac { 64 } { 729 y ^ { 6 } }$
B) $- \frac { 27 y ^ { 6 } } { 8 }$
C) $\frac { 8 } { 27 y ^ { 6 } }$
D) $\frac { 3 y ^ { 2 } } { 2 }$

Question

Quizplus · Accepted Answer

First, apply the negative exponent rule by taking the reciprocal of the base and changing the sign of the exponent: $\left( \frac { 16 } { 81 y ^ { 8 } } \right) ^ { \frac { 3 } { 4 } }$. Then, apply the fractional exponent by taking both the cube root and raising to the third power: $\frac { 2 ^ { 3 } } { 3 ^ { 3 } y ^ { 6 } } = \frac { 8 } { 27 y ^ { 6 } }$.

Simplify (81y816)−34\left( \frac { 81 y ^ { 8 } } { 16 } \right) ^ { - \frac { 3 } { 4 } }(1681y8​)−43​

Simplify $\left( \frac { 81 y ^ { 8 } } { 16 } \right) ^ { - \frac { 3 } { 4 } }$