Properties of Exponents

When multiplying like bases, add the exponents: (x^m)(x^n) = $$x^{m+n}$$ .

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

Distribute the exponent to each factor in the product: $$(xy)^m = x^m y^m$$ .

Distribute the exponent to both the numerator and the denominator: $$\left(\frac{x}{y}\right)^m$$ = $$\frac{x^m}{y^m}$$ .

When dividing like bases, subtract the exponents: $$\frac{x^m}{x^n}$$ = $$x^{m-n}$$ .

Any non-zero base raised to the zero power is 1: $$x^0 = 1$$ .

A negative exponent indicates a reciprocal: $$x^{-m}$$ = $$\frac{1}{x^m}$$ .

Use the rules of exponents to simplify expressions involving powers.

Rules that help simplify expressions with powers, such as product, quotient, and power properties.

Add the exponents when multiplying powers with the same base.