Precal Laws of Exponents

Front

What is the law of exponents that states \( a^m \cdot a^n = a^{m+n} \)?

Back

This is the Product of Powers Property.

Front

What is the law of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \)?

Back

This is the Quotient of Powers Property.

Front

What is the law of exponents that states \( (a^m)^n = a^{m \cdot n} \)?

Back

This is the Power of a Power Property.

Front

What is the law of exponents that states \( a^0 = 1 \) for any non-zero number \( a \)?

Back

This is the Zero Exponent Rule.

Front

What is the law of exponents that states \( a^{-n} = \frac{1}{a^n} \)?

Back

This is the Negative Exponent Rule.

Front

Simplify the expression: \( \frac{-3x^2yz^3}{9z^{10}x} \)

Back

\( -\frac{xy}{3z^7} \)

Front

Simplify the expression: \( \frac{xy(24x^2y^3w)}{36y^5w^2} \)

Back

\( \frac{2x^3}{3yw} \)

Front

Simplify the expression: \( \frac{1}{a^{-5}} \)

Back

\( a^5 \)

Front

Simplify the expression: \( \frac{20(x^{-2})^3}{5(x^{-4})^{-3}} \)

Back

\( \frac{4}{x^{18}} \)

Front

What is the law of exponents that states \( a^m \cdot b^m = (ab)^m \)?

Back

This is the Power of a Product Property.