What is the Product-of-Powers Property?

Question

This question is math- related, and I'm having difficulty understanding this concept, which I need for one of my math problems.

Answer 1

Product of Powers Property: This property states that to multiply powers having the same base, add the exponents.

For example, take x² times x³.

x² is x times x.

x³ is x times x times x.

x² times x³ is therefore (x times x) times (x times x times x), or x to the fifth power.

So when you multiply two numbers with the same base, you add the exponents.

Answer 2

It is either
a^c * b^c = (a*b)^c
or
a^b * a^c = a^(b+c).

Both are true, the first one is for the case when the exponents are the same and second one is for the case when the bases are the same.