Question

Applying Properties of Exponents In Exercise,use the properties of exponents to simplify the expression.

Answer 1

Answer:

$1. ~e^5\\2. ~e^{\frac{3}{2}}\\3. ~e^6\\4.~ e^7$

Step-by-step explanation:

We have to simplify the given exponential expressions

Exponential properties:

$e^0 =1\\e^a.e^b = e^{a+b}\\\\\displaystyle\frac{e^a}{e^b} = e^{a-b}\\\\(e^a)^b = e^{ab\\\\e^{-a} = \frac{1}{e^a}$

Simplification takes place in the following manner:

1)

$(e^2)^\frac{5}{2}\\\text{Applying the exponential property}\\\\=e^{2\times \frac{5}{2}}\\= e^5$

2)

$(e^2)(e^{\frac{1}{2}})\\\text{Using the exponential propert}\\\\= e^{2 + \frac{1}{2}} = e^{\frac{3}{2}}$

3)

$(e^{-2})^{-3}\\= e^{-2\times -3}\\=e^6$

4)

$\displaystyle\frac{e^5}{e^{-2}}\\\\\text{Using exponential properties}\\\\= e^{5-(-2)} = e^7$