Question

What are the values of a and b in the equation (4x^a)^b = 256/x^8

Answer 1

b = 4 and a = -2

(4x^-2)^4
= 4^4 x^-8
= 4^4 / x^8
= 256/x^8

Answer 2

The value of a is -2 and the value of b is 4.

Explanation:

Given expression is,

`(4x^a)^b = (256)/(x^8)`

Using
`(ab)^m=a^m.b^n` on left side,

`4^b(x)^(ab)=(4^4)/(x^8)` (
`4^4 = 256` )

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

`4^b(x)^(ab)=4^4 (x)^(-8)`

By comparing both sides,

We get,

b = 4 and ab = -8

⇒ a = -2

Hence, the value of a is -2 and the value of b is 4.