exponent operations

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

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

When raising a product to a power, you distribute the exponent to each factor. For example, $$(ab)^n = a^n \times b^n$$ .

When raising a quotient to a power, you distribute the exponent to the numerator and denominator. For example, $$\frac{a}{b}^n = \frac{a^n}{b^n}$$ .

$$a^{5-2} = a^3$$ .

$$16n^{16}$$ .

$$81x^{12}$$ .

$$10n^8$$ .

$$8x^6y^{12}$$ .

$$x^{3+4} = x^7$$ .