How do you find the prime factorization of 81?

Answer 1

Answer 3^4

There are many ways to do it. Here is one that I find intuitive and simpler than some others.

You note that 81 is 9x9 and that 9 is 3x3. So 81 = (3^2) (3^2 )

Then using the laws of exponents we remember that when we multiply numbers with exponents, we add the exponents. So the answer is 3^4

81 is 9 x 9

9 is 3 x 3

So 81 must be 3 x 3 x 3 x 3