Simplify.
-$\frac { 1 } { e ^ { 5 } }$ ∙ $\frac { \mathrm { e } ^ { 3 } } { 2 }$ ∙ $e ^ { 4 x - 1 }$
A) $\frac { e ^ { 12 x - 3 } } { 2 e ^ { 5 } }$
B) $\frac { 1 } { 2 }$ $e ^ { 4 x - 3 }$
C) $\frac { 1 } { 2 }$ $e ^ { 12 x - 8 }$
D) cannot be simplified

Question

Simplify. 
-$\frac { 1 } { e ^ { 5 } }$ ∙ $\frac { \mathrm { e } ^ { 3 } } { 2 }$ ∙ $e ^ { 4 x - 1 }$
A) $\frac { e ^ { 12 x - 3 } } { 2 e ^ { 5 } }$
B) $\frac { 1 } { 2 }$ $e ^ { 4 x - 3 }$
C) $\frac { 1 } { 2 }$ $e ^ { 12 x - 8 }$
D) cannot be simplified

Quizplus · Accepted Answer

When simplifying expressions with exponents, we can use the property that $e^{a} \cdot e^{b} = e^{a+b}$. Thus, combining the exponents gives $e^{3} \cdot e^{4x-1} = e^{3+4x-1} = e^{4x+2}$. However, since there's also a division by $e^{5}$, we subtract the exponent in the denominator from the exponent in the numerator: $e^{4x+2-5} = e^{4x-3}$. The coefficient $\frac{1}{2}$ remains unchanged, leading to the simplified expression $\frac{1}{2} e^{4x-3}$.

Simplify - 1e5\frac { 1 } { e ^ { 5 } }e51​

Simplify
- $\frac { 1 } { e ^ { 5 } }$