Simplify the expression. $\left( - \frac { 8 } { 27 } \right) ^ { - \frac { 4 } { 3 } }$
A) $\frac { 16 } { 81 }$
B) $\frac { 81 } { 16 }$
C) $\frac { 2 } { 3 }$
D) $\left( \frac { 3 } { 2 } \right) ^ { 4 }$
E) $\frac { 3 } { 2 }$

Question

Quizplus · Accepted Answer

To simplify $\left( - \frac { 8 } { 27 } \right) ^ { - \frac { 4 } { 3 } }$, first recognize that $-\frac{8}{27}$ is the cube of $-\frac{2}{3}$. Raising this to the power of $-\frac{4}{3}$ is equivalent to taking the cube root and then raising to the power of $-4$, which inverts the fraction and squares it. Thus, $\left( - \frac { 2 } { 3 } \right)^{-4} = \left( \frac { 3 } { 2 } \right)^{4} = \frac { 81 } { 16 }$.

Simplify the Expression (−827)−43\left( - \frac { 8 } { 27 } \right) ^ { - \frac { 4 } { 3 } }(−278​)−34​

Simplify the Expression $\left( - \frac { 8 } { 27 } \right) ^ { - \frac { 4 } { 3 } }$