Question

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

(a) (e2)5/2
(b) (e2)(e1/2)
(c) (e-2)-3
(d) e^5/e^-2

Answer 1

`1. ~e^5\\2. ~e^{(3)/(2)}\\3. ~e^6\\4.~ e^7`

Explanation:

We have to simplify the given exponential expressions

Exponential properties:

`e^0 =1\\e^a.e^b = e^(a+b)\\\\\displaystyle(e^a)/(e^b) = e^(a-b)\\\\(e^a)^b = e^{ab\\\\e^(-a) = (1)/(e^a)`

Simplification takes place in the following manner:

1)

`(e^2)^(5)/(2)\\\text{Applying the exponential property}\\\\=e^{2* (5)/(2)}\\= e^5`

2)

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

3)

`(e^(-2))^(-3)\\= e^(-2* -3)\\=e^6`

4)

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