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2^x = 7, then 2^2x =? a)49 b)7 c)128 d)64 e)32

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by MartyMurray » Thu Sep 29, 2016 8:57 am
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.
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by Matt@VeritasPrep » Thu Sep 29, 2016 6:18 pm
Another approach:

(aᵇ)ᶜ = (aᶜ)ᵇ

so

(2²)ˣ = (2ˣ)²

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