Math - Laws of Exponents

Vocabulary flashcards covering the definitions and formulas for the laws of exponents based on the lecture notes.

Product of Powers

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

Quotient of Powers

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

Power of a Power

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

Power of a Product

When raising a product to a power, apply the exponent to each part: $(ab)^n = a^n \cdot b^n$.

Power of a Quotient

When raising a quotient to a power, apply the exponent to the numerator and denominator: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.

Zero Exponent

Any non-zero base raised to $0$ is one: $a^0 = 1$.

Negative Exponent

Indicates the reciprocal of the base raised to the absolute value of the exponent: $a^{-n} = \frac{1}{a^n}$.

Fractional Exponents

Indicates a root: $a^{\frac{m}{n}} = \sqrt[n]{a^m}$.