Question

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

(a) (e-3)2/3
(b) e^4/e^-1/2
(c) (e-2)-4
(d) (e-4)(e-3/2)

Answer 1

`1.~e^(-2) \\2.~e^{(7)/(2)}\\3.~e^8\\4.~e^{(-11)/(2)}`

Explanation:

We have to simplify the given exponential exponents.

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:

a)

`(e^(-3))^(2)/(3)\\(e^a)^b = e^(ab)\\=e^{-3* (2)/(3)}\\=e^(-2)`

b)

`(e^4)(e^{(-1)/(2)})\\e^a.e^b = e^(a+b)\\=e^{(4+(-1)/(2))} \\= e^{(7)/(2)}`

c)

`(e^(-2))^(-4)\\(e^a)^b = e^(ab)\\= e^(-2* -4)\\=e^8`

d)

`(e^(-4))(e^{(-3)/(2)})\\e^a.e^b = e^(a+b)\\=e^{(-4+(-3)/(2))} \\= e^{(-11)/(2)}`