Question

Why do we add the exponents when multiplying monomials that have the same base? Please help me thank you.

Answer 1

Positive whole number exponents represent repeated multiplication of the base.

For example, 2^3 means 2*2*2. We have 3 copies of the base 2 multiplied

Another example: 2^4 = 2*2*2*2 showing four copies of '2' multiplied

When multiplying 2^3 with 2^4, we have 3+4 = 7 copies of 2 multiplied overall. Notice I added the exponents. So 2^3*2^4 = 2^(3+4) = 2^7

The general rule is that a^b*a^c = a^(b+c)

Answer 2

When multiplying 2 monomials together like (x^(2)*x^(2). We add the exponents together because what you are actually doing is (x*x*x)*(x*x) if you attempted to add the base  you would be instead add x^(3) +x^(2) and within algebra, you are taught you can't add these terms together because they both have a different degree to them. Hope that helps clarify the difference.