What is the smallest integer n for which 16n = 412?
A)2
B)4
C)6
D)12

Question

Quizplus · Accepted Answer

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:
am x an = am+n, am / an = a m-n , (am ) n = a m x n , (am ) 1/n = a m/ n

What Is the Smallest Integer N for Which 16n =