Question

Question #205a2

Answer 1

`[(2x^2)^3]^5=32768x^30`

Explanation:

`(x^a)^b=(x^a) * (x^a) * ... * (x^a)` , for b times`= x^(a*b)`

`=>`
`[(2x^2)^3]^5=`
`= [(2x^2) * (2x^2) * (2x^2)]^5 =`
`= [(2^1 * 2^1 *2^1) * (x^2 * x^2 * x^2)]^5 =`
`= [(2^3) * (x^(2*3))]^5 =`
`= [(8) * (x^6)]^5 =`
`= [8x^6]^5`

in the same way of thinking:
`= [8x^6]^5=...=8^5*x^(6*5)=32768x^30`