Problem Solving

2^x = 7, then 2^2x =?

a)49
b)7
c)128
d)64
e)32

Please assist with above problem.

Exponents of the same base can be added when powers of that base are multiplied.

So 2²ˣ = 2ˣ * 2ˣ.

So if 2²ˣ = 7, then 2²ˣ = 7 x 7 = 49.

Alternatively, you can express 2²ˣ in this way, (2ˣ)², because to get from the second expression to the first you would multiply the exponent inside the parentheses by the exponent outside the parentheses.

If 2ˣ = 7, then 2²ˣ = (2ˣ)² = 49.

The correct answer is A.

Another approach:

(aᵇ)ᶜ = (aᶜ)ᵇ

so

(2²)ˣ = (2ˣ)²

and we're told that (2ˣ)² = 49, so that's our answer!