Question

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

(a) (e6) (e - 3)
(b) (e - 2) - 5
(c) (e^6/e^2)^-1
(d) (e3)4/3

Answer 1

Answer: (a)
`e^3`

(b)
`e^(10)`

(c)
`(1)/(e^4)`

(d)
`e^(4)`

Explanation:

Properties of exponents :

1)
`a^m* a^n=a^(m+n)`

2)
`(a^m)/(a^n)=a^(m-n)`

3)
`(a^m)^n=a^(mn)`

4)
`a^(-n)=(1)/(a^n)`

Now , we simplify the given expression using the above properties.

a)
`(e^6)(e^(-3))`

`=e^(6+(-3))` [By property (1)]

`=e^(6-3)=e^3` [∵ (+)(-)=(-)]

b)
`(e^(-2))^(-5)`

`=e^(-2*-5)` [By property (3)]

`=e^(10)` [∵ (-)(-)=(+)]

c)
`((e^6)/(e^2))^(-1)`

`=(e^(6-2))^(-1)` [By property (2)]

`=(e^(4))^(-1)`

`=(1)/(e^4)` [By property (4)]

d)
`(e^3)^{(4)/(3)}`

`=e^{3*(4)/(3)}` [By property (3)]

`=e^(4)`