12^k + 6^k = | GMAT Sprint

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PS · Problem Solving

505-555

Exponents/Powers

$12^k + 6^k =$

Correct answer marked below

6(2^k + 1)

6^k(2^k + 1)

Correct

6^k*4^k

18^k

18^{2k}

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Explanation

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Official Explanation

Official

12^k + 6^k =

6(2^k + 1)

6^k(2^k + 1)

6^k*4^k

18^k

18^{2k}

…

Comments

LangJan 30, 2024

thanks for the answer

anumulaFeb 12, 2025

greatt question!

ArhanSep 10

how do you know to split 12 into 6 and 2 instead of like 4 and 3? is it just because of the 6^k term?

ArinSep 16

yeah basically, whenever you have two terms with a common base lurking, factor so one of them matches. here you want that 6^k to pop out

What this question tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).