How are the properties of exponents used when multiplying two monomials?

How are the properties of exponents used when dividing two monomials?

nᵃ n=base, a=power

When multiplying two monomials of the same base, you add the exponents of the terms and don't change the base.

nᵃ*nᵇ=nᵃ⁺ᵇ

When dividing two monomials of the same base, you subtract the power of the denominator from the power of the numerator and don't change the base.

nᵃ/nᵇ=nᵃ⁻ᵇ

properties of exponent cannot be used if the monomials don't have the same base.