ICE Special Agent Exam Prep

Answer: C 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
It is given 16ⁿ = 4¹²
So we can write
4²ⁿ = 4¹²
Base is same 4 and hence 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}