Properties of Exponents

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

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 eq 0@@.

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, $$a^{-n} = \frac{1}{a^n}$$ .

$$\frac{-3}{m^4}$$ .

$$175a^{14}b^2$$ .

$$10m^6$$ .

$$64x^{18}y^6$$ .