Simplify the expression. $$\left( - \frac { 243 } { 1024 } \right) ^ { \frac { 1 } { 5 } }$$

Question

Quizplus · Accepted Answer

We can simplify the expression by finding the fifth root of both the numerator and the denominator separately: $$\left( -\frac{243}{1024} \right)^\frac{1}{5} = \frac{\sqrt[5]{-243}}{\sqrt[5]{1024}}$$
Note that $\sqrt[5]{-243} = -3$ and $\sqrt[5]{1024} = 2$, so we have $$\frac{\sqrt[5]{-243}}{\sqrt[5]{1024}} = \frac{-3}{2} = \boxed{\textbf{(B) }-\frac{3}{4}}.$$

Simplify the Expression (−2431024)15\left( - \frac { 243 } { 1024 } \right) ^ { \frac { 1 } { 5 } }(−1024243​)51​

Simplify the Expression $\left( - \frac { 243 } { 1024 } \right) ^ { \frac { 1 } { 5 } }$