Simplify the expression. All variables represent positive real numbers. $- \left( 16 x ^ { 2 } \right) ^ { - \frac { 3 } { 2 } }$
A) $- \frac { 1 } { 64 x ^ { 3 } }$
B) $- \frac { 16 } { x ^ { 3 } }$
C) $- \frac { 64 } { x ^ { 3 } }$
D) $- \frac { x ^ { 2 } } { 64 }$
E) $- \frac { x ^ { 3 } } { 64 }$

Question

Quizplus · Accepted Answer

The expression simplifies by applying the negative exponent rule, which turns the expression into a fraction and the exponent into a positive. The expression $- (16x^2)^{-\frac{3}{2}}$ simplifies to $- \frac{1}{(16x^2)^{\frac{3}{2}}}$. Since $16 = 4^2$, and raising to the power of $\frac{3}{2}$ is equivalent to taking the square root and then cubing, the expression simplifies further to $- \frac{1}{(4^2x^2)^{\frac{3}{2}}} = - \frac{1}{4^3x^3} = - \frac{1}{64x^3}$.

Simplify the Expression −(16x2)−32- \left( 16 x ^ { 2 } \right) ^ { - \frac { 3 } { 2 } }−(16x2)−23​

Simplify the Expression $- \left( 16 x ^ { 2 } \right) ^ { - \frac { 3 } { 2 } }$