Question

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

(a) (45)(42)
(b) (72)3
(c) 2- 4
(d) 3^8/3^4

Answer 1

(a)
`4^7`

(b)
`7^6`

(c)
`(1)/(16)`

(d)
`3^(4)`

Explanation:

We need to simplify the given expressions.

(a)

Consider the given expression is

`(4^5)(4^2)`

Using the property of exponent, we get

`=4^(5+2)`
`[\because a^ma^n=a^(m+n)]`

`=4^7`

(b)

Consider the given expression is

`(7^2)^3`

Using the property of exponent, we get

`=7^(2* 3)`
`[\because (a^m)^n=a^(mn)]`

`=7^6`

(c)

Consider the given expression is

`2^(-4)`

Using the property of exponent, we get

`=(1)/(2^(4))`
`[\because a^(-n)=(1)/(a^n)]`

`=(1)/(16)`

(d)

Consider the given expression is

`(3^8)/(3^4)`

Using the property of exponent, we get

`=3^(8-4)`
`[\because (a^m)/(a^n)=a^(m-n)]`

`=3^(4)`