Exponent Rules

When multiplying two expressions with the same base, add the exponents: a^m * a^n = a^(m+n).

When dividing two expressions with the same base, subtract the exponents: a^m / a^n = a^(m-n).

When raising a power to another power, multiply the exponents: (a^m)^n = a^(m*n).

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

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/(a^n) (where a ≠ 0).

Apply the exponent rules in the correct order: simplify multiplication and division first, then apply power rules.

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

When raising a quotient to a power, apply the exponent to both the numerator and the denominator: (a/b)^n = a^n / b^n.

Combine the exponents: x^m * x^n = x^(m+n).

Multiply the exponents: (x^m)^n = x^(m*n).