Exponent Rules

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

6^8 (using the Quotient Rule: 30 - 22 = 8).

Keep the base the same and subtract the exponents.

1 (e.g., (-9)^0 = 1).

$$\frac{1}{a^2}$$ .

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

10^12 (using the Product Rule: 5 + 7 = 12).

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

2^12 (using the Power of a Power Rule: 3 * 4 = 12).

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