exponent operations

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

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: $$a^{-n} = \frac{1}{a^n}$$ .

$$\frac{5p^3}{3}$$ .

$$a^{8-2} = a^6$$ .

$$b^{13-7} = b^6$$ .

$$c^{5-5} = c^0 = 1$$ .

$$\frac{1}{2}x^{4-1}y^{2-1} = \frac{1}{2}x^3y$$ .