Exponent Laws

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

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

12a^5b^4.

n^6.

$$x^5 \cdot y^5$$ .

2^2.

When raising a product to a power, you raise each factor to that power. For example, $$(ab)^n = a^n b^n$$ .

When raising a power to another power, you multiply the exponents. For example, $$(a^m)^n = a^{m \cdot n}$$ .

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

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