GMAT Math Practice Test #1

Answer: C - 6

First convert 16ⁿ to the same base 4. You know 16 = 4 x 4 = 4² , so you can write 16ⁿ = (16)ⁿ = (4²)ⁿ = 4²ⁿ. We know that given 16ⁿ = 4¹², so we can write 4²ⁿ = 4¹² Since both have ase 4, their powers are equal 2n = 12, or n = 6.

Key takeaway: When solving problems involving exponents, base is to be seen carefully. It is easy to simplify, as long as they have the same base. Remember following simple formulae:

a^m x aⁿ = a^m+n, a^m / aⁿ = a ^m-n , (a^m ) ⁿ = a ^{m x n} , (a^m ) ^1/n = a ^{m/ n}