Exponent Rules

To rewrite a negative exponent as a positive exponent, take the reciprocal of the base. For example, $$a^{-n} = \frac{1}{a^{n}}$$ .

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

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

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

Any non-zero base raised to the power of zero equals one. For example, $$a^0 = 1$$ , where a ≠ 0.

$$9$$ .

$$x^8$$ .

$$x^4$$ .

The result is positive. For example, $$(-2)^2 = 4$$ .

The result is negative. For example, $$(-2)^3 = -8$$ .