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

Answer:

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

Step-by-step explanation:

Given expression is,

$(4x^a)^b = \frac{256}{x^8}$

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

$4^b(x)^{ab}=\frac{4^4}{x^8}$     ( $4^4 = 256$ )

Using $a^m=\frac{1}{a^{-m}}$,

$4^b(x)^{ab}=4^4 (x)^{-8}$

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.