Question

Applying properties of Exponents in exercise,use the properties of exponents to simplify the expression.See example 1.

(a) (43)(42)
(b) (1/4)^2(4^2)
(c) (46)1/2
(d) [(8-1)(82/3)]3

Answer 1

Answer: a) 1024, b) 1, c) 64 and d) 0.125.

Explanation:

Since we have given that

(a)
`(4^3)(4^2)`

As we know that

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

So, it becomes,

`4^3* 4^2=4^(3+2)=4^5=1024`

(b)
`((1)/(4))^2(4^2)`

As we know that

`a^(-m)=(1)/(a^m)`

`((1)/(4))^2(4^2)=4^-2* 4^2=4^(-2+2)=4^0=1`

c)
`(4^6)1/2`

As we know that

`(4^6)^{(1)/(2)}\\\\=4^{(6)/(2)}\\\\=4^3\\\\=64`

(d)
`[(8^(-1))(8^{(2)/(3)})]^3`

As we know that

`[(8^(-1))(8^{(2)/(3)})]^3\\\\=[8^{-1+(2)/(3)}]^3\\\\=[8^{(-1)/(3)}]^3\\\\=8^(-1)\\\\=(1)/(8)=0.125`

Hence, a) 1024, b) 1, c) 64 and d) 0.125.