Simplify the expression. All variables represent positive real numbers. $\left( 4 x ^ { 4 } \right) ^ { \frac { 3 } { 2 } }$
A) $\left( 2 x ^ { 2 } \right) ^ { 3 }$
B) $8 \left( x ^ { 4 } \right) ^ { \frac { 3 } { 2 } }$
C) $8 x ^ { 6 }$
D) $8 x ^ { 12 }$
E) $8 x ^ { 2 }$

Question

Quizplus · Accepted Answer

To simplify $\left( 4 x ^ { 4 } \right) ^ { \frac { 3 } { 2 } }$, first apply the power to both the coefficient and the variable: $4^{3/2} \cdot (x^4)^{3/2}$. Since $4^{3/2} = 8$ and $(x^4)^{3/2} = x^{4 \cdot 3/2} = x^6$, the simplified expression is $8x^6$.

Simplify the Expression (4x4)32\left( 4 x ^ { 4 } \right) ^ { \frac { 3 } { 2 } }(4x4)23​

Simplify the Expression $\left( 4 x ^ { 4 } \right) ^ { \frac { 3 } { 2 } }$