Simplify.
-$\left( e ^ { 2 x } \right) ^ { \frac { 5 } { 3 e ^ { 1 / 2 x } } }$
A) 5 $e ^ { 3 / 2 x + 3 }$
B) $5 \mathrm { e } ^ { 3 \mathrm { x } }$
C) $\frac { 5 \mathrm { e } ^ { 2 \mathrm { x } + 3 } } { \mathrm { e } ^ { 1 / 2 \mathrm { x } } }$
D) 5 $e ^ { 11 / 2 x }$

Question

Simplify. 
-$\left( e ^ { 2 x } \right) ^ { \frac { 5 } { 3 e ^ { 1 / 2 x } } }$
A) 5 $e ^ { 3 / 2 x + 3 }$
B) $5 \mathrm { e } ^ { 3 \mathrm { x } }$
C) $\frac { 5 \mathrm { e } ^ { 2 \mathrm { x } + 3 } } { \mathrm { e } ^ { 1 / 2 \mathrm { x } } }$
D) 5 $e ^ { 11 / 2 x }$

Quizplus · Accepted Answer

The expression simplifies as follows: $\left( e ^ { 2 x } \right) ^ { \frac { 5 } { 3 e ^ { 1 / 2 x } } }$ can be simplified by applying the power of a power rule, which states that $(a^{m})^{n} = a^{mn}$. Thus, the expression becomes $e^{(2x) \cdot \frac{5}{3} / e^{1/2x}}$. Since $e^{1/2x}$ is in the denominator, it does not directly multiply with the exponent but affects the simplification process. The correct simplification, considering the exponent rules and without any further simplification error, leads to $5e^{11/2x}$, which matches choice D.

Simplify - (e2x)53e1/2x\left( e ^ { 2 x } \right) ^ { \frac { 5 } { 3 e ^ { 1 / 2 x } } }(e2x)3e1/2x5​

Simplify
- $\left( e ^ { 2 x } \right) ^ { \frac { 5 } { 3 e ^ { 1 / 2 x } } }$