If 2a-b=4, what is the value of 4^a/2^b?

Answer 1

I'll start with the 2nd part.

Since 4 = 2², 4^a = 2^2a, so we have 2^2a/2^b.

Remembering that with the same base, when we divide, we subtract the exponents.

2^2a/2^b = 2^{2a - b}

Since 2a - b = 4, 2^{2a - b} = 2⁴ = 16

Answer 2

To answer this question, a student should understand the laws of exponents(indices)

4^a can be written as 2^2a

so 4^a /2^b = 2^2a /2^b

when dividing numbers with the same base, you subtract the exponents

2^2a /2^b = 2^2a-b

But 2a-b = 4

Therefore, 4^a /2^b = 2^2a-b = 2⁴ =16