Question

What are three ways to express 3 to the 5th power as a product of powers

Answer 1

Remember
$(x^m)(x^n)=x^{m+n}$

so find numbers that add to 5
0+5

2+2+1

1+4

so we can write
$(3^0)(3^5)=3^5$
$(3^2)(3^2)(3^1)=3^5$
$(3^1)(3^4)=3^5$
those are 3 ways to express $3^5$ as a product of powers