Simplify the expression. $\left( \frac { 64 } { 125 } \right) ^ { \frac { 4 } { 3 } }$
A) $\frac { 4 } { 5 }$
B) $\frac { 1,024 } { 3,125 }$
C) $\frac { 256 } { 625 }$
D) $\frac { 625 } { 256 }$
E) $\frac { 259 } { 628 }$

Question

Quizplus · Accepted Answer

We can simplify the expression by finding the fourth power of both the numerator and the denominator separately, and then taking the cube root of the resulting fraction. $64^4=(2^6)^4=2^{24}$ and $125^3=(5^3)^3=5^{9}$. So $\left(\frac{64}{125}\right)^{\frac{4}{3}}=\left(\frac{2^{24}}{5^9}\right)^{\frac{1}{3}}=\frac{2^8}{5^3}=\frac{256}{625}$. Therefore, the answer is choice C.

Simplify the Expression (64125)43\left( \frac { 64 } { 125 } \right) ^ { \frac { 4 } { 3 } }(12564​)34​

Simplify the Expression $\left( \frac { 64 } { 125 } \right) ^ { \frac { 4 } { 3 } }$