Evaluate the given expression. $$\left( \frac { 256 } { 625 } \right) ^ { 5 / 4 }$$
A) $\frac { 1,024 } { 3,125 }$
B) $\frac { 4 } { 5 }$
C) $\frac { 1,024 } { 625 }$
D) $\frac { 256 } { 625 }$

Question

Quizplus · Accepted Answer

The expression can be simplified by taking the 4th root of both the numerator and the denominator and then raising the result to the 5th power. The 4th root of 256 is 4, and the 4th root of 625 is 5. Raising both to the 5th power gives $4^5 = 1024$ and $5^5 = 3125$, resulting in $\frac{1024}{3125}$.

Evaluate the Given Expression (256625)5/4\left( \frac { 256 } { 625 } \right) ^ { 5 / 4 }(625256​)5/4

Evaluate the Given Expression $\left( \frac { 256 } { 625 } \right) ^ { 5 / 4 }$