Mixed Review Exponent Laws

When multiplying two powers with the same base, you add the exponents. For example, $$a^m \times a^n = a^{m+n}$$ .

The power of a product rule states that when raising a product to a power, you can distribute the exponent to each factor. For example, $$(ab)^n = a^n b^n$$ .

The power of a quotient rule states that when raising a quotient to a power, you can distribute the exponent to the numerator and denominator. For example, $$\frac{a}{b}^n = \frac{a^n}{b^n}$$ .

Any non-zero number raised to the power of zero is equal to one. For example, $$a^0 = 1$$ , where a ≠ 0.

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, $$a^{-n} = \frac{1}{a^n}$$ .

-8r^{13}.

Any expression (except zero) raised to the power of zero equals one. For example, $$(5^3 x^2 y^4)^0 = 1$$ .

1.

When multiplying powers with the same exponent, you multiply the bases. For example, $$a^n \times b^n = (ab)^n$$ .

7b^3 a^5.