Properties of Exponents (and Radicals!)

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

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

When raising a product to a power, apply the exponent to each factor: $$(ab)^n = a^n \times b^n$$ .

Any non-zero number raised to the power of zero equals one: $$a^0 = 1$$ (where a ≠ 0).

A negative exponent indicates the reciprocal: $$a^{-n} = \frac{1}{a^n}$$ (where a ≠ 0).

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

$$x^{28-2}y^{12-1} = x^{26}y^{11}$$ .

The nth root of a number can be expressed as a fractional exponent: @@ oot{n}{a} = a^{rac{1}{n}}@@.

$$x^{\frac{7}{3}}$$ .

$$x^{4+12} = x^{16}$$ .