Question

why does this make sense?
you use the power of a product law of exponents to combine the exponents; this law says to add the exponents.
you use the power of a power law of exponents to combine the exponents; this law says to multiply the exponents.
you use the product of powers law of exponents to combine the exponents; this law says to add the exponents.

Explanation:

First, clarify the exponent rules:

1. Power of a product: $(ab)^n = a^n b^n$ (does not add exponents of same base)
2. Power of a power: $(a^m)^n = a^{m \times n}$ (multiplies exponents)
3. Product of powers: $a^m \times a^n = a^{m+n}$ (adds exponents of the same base). This rule is used when combining like bases multiplied together, which is the standard scenario for adding exponents.

Answer:

You use the product of powers law of exponents to combine the exponents; this law says to add the exponents.