Rules of Exponents Flashcard:

Front

Rewrite using a positive exponent: w^{-13}

Back

\frac{1}{w^{13}}

Front

Simplify: 5^{-2}

Back

\frac{1}{25}

Front

Simplify: (z^5)^5

Back

z^{25}

Front

Simplify: 7v^{3} * 10u^{3}v^{5}

Back

70u^{3}v^{8}

Front

Definition: Negative Exponent

Back

A negative exponent indicates that the base should be taken as the reciprocal raised to the opposite positive exponent.

Front

Definition: Zero Exponent

Back

Any non-zero number raised to the power of zero equals one.

Front

Property: Product of Powers

Back

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

Front

Property: Power of a Power

Back

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

Front

Property: Power of a Product

Back

When raising a product to a power, raise each factor to the power: (ab)^n = a^n * b^n.

Front

Example: Simplifying Negative Exponents

Back

Example: x^{-3} = \frac{1}{x^{3}}.