Negative Exponents

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

$$\frac{1}{w^{13}}$$ .

Any non-zero number raised to the power of zero equals 1. For example, $$(-9)^0 = 1$$ .

$$\frac{1}{16}$$ .

$$\frac{1}{27}$$ .

$$12^{-4}$$ .

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

When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$ .

When raising a power to another power, multiply the exponents: $$(a^m)^n = a^{m \times n}$$ .

0 raised to any positive exponent is 0. For example, $$0^3 = 0$$ .