Exponent Laws Overview

Front

Definition of Exponent

Back

An exponent refers to the number of times a number (the base) is multiplied by itself.

Front

Product of Powers Rule

Back

a^m · aⁿ = a^m+n

^{When multiplying numbers with the same base and different exponents, you can add the exponents to simplify.}

Front

Quotient of Powers Rule

Back

a^m / aⁿ = a^m-n

^{When dividing numbers with the same base and different exponents, you can subtract the exponents to simplify.}

Front

Power of a Power Rule

Back

(a^m)ⁿ = a^mn

^{When exponents are raised to another power, multiply the exponents to simplify.}

Front

Power of a Product Rule

Back

(ab)ⁿ = aⁿ · bⁿ

^{When there are multiple terms inside the parentheses, the exponent applies to each one.}

Front

Power of a Quotient Rule

Back

(a/b)ⁿ = aⁿ/bⁿ

^{When a fraction is raised to an exponent, it applies to both the numerator and the denominator.}

Front

Fractional Exponent to Radical

Back

a^1/n = ⁿ√a

Front

Zero Exponent Rule

Back

a⁰ = 1

A number raised to the power of zero is 1.

Front

Negative Exponent Rule

Back

a^-n = 1/aⁿ

^{You have to make your exponents positive by taking the reciprocal and then simplify.}

Front

Simplify: 7⁰

Back

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