Question

What are the values of a and b in the equation (4 x Superscript a Baseline) Superscript b Baseline = StartFraction 256 Over x Superscript 8 EndFraction?

a = 2, b = 4
a = negative 2, b = 4
a = negative 2, b = negative 4
a = 2, b = negative 4

Answer 1

a = negative 2, b = 4

Explanation:

We want to find the value of a and b in the equation:

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

We rewrite the RHS to get:

`(4 {x}^(a))^(b) = 256{x}^( - 8)`

`(4 {x}^(a))^(b) = {4}^(4) {x}^( - 8)`

`(4 {x}^(a))^(b) = ( {4} {x}^( - 2))^(4)`

We now compare to have a=-2 and b=4