Simplify.
-$\sqrt { \frac { e ^ { ( 1 / 2 ) x } \cdot e ^ { ( 3 / 2 ) x } } { e ^ { - 2 x } } }$
A) $\frac { 1 } { e ^ { 2 x } }$
B) $e ^ { - 6 x }$
C) $e ^ { ( 1 / 2 ) x }$
D) $e ^ { - 10 x }$
E) none of these

Question

Simplify. 
-$\sqrt { \frac { e ^ { ( 1 / 2 ) x } \cdot e ^ { ( 3 / 2 ) x } } { e ^ { - 2 x } } }$
A) $\frac { 1 } { e ^ { 2 x } }$
B) $e ^ { - 6 x }$
C) $e ^ { ( 1 / 2 ) x }$
D) $e ^ { - 10 x }$
E) none of these

Quizplus · Accepted Answer

First, simplify the expression inside the square root using the properties of exponents: $\sqrt { \frac { e ^ { ( 1 / 2 ) x } \cdot e ^ { ( 3 / 2 ) x } } { e ^ { - 2 x } } } = \sqrt { e ^ { ( 1 / 2 + 3 / 2 - ( - 2 ) ) x } } = \sqrt { e ^ { 4 x } }$. The square root of $e^{4x}$ is $e^{2x}$, which is not listed among the options, so the correct answer is E, none of these.

Simplify - e(1/2)x⋅e(3/2)xe−2x\sqrt { \frac { e ^ { ( 1 / 2 ) x } \cdot e ^ { ( 3 / 2 ) x } } { e ^ { - 2 x } } }e−2xe(1/2)x⋅e(3/2)x​​

Simplify
- $\sqrt { \frac { e ^ { ( 1 / 2 ) x } \cdot e ^ { ( 3 / 2 ) x } } { e ^ { - 2 x } } }$