QUOTIENT OF POWERS PRACTICE SET

Front

What is the Quotient of Powers Property?

Back

The Quotient of Powers Property states that when dividing two powers with the same base, you subtract the exponents: \( a^m \div a^n = a^{m-n} \).

Front

Simplify: \( \frac{x^5}{x^2} \)

Back

\( x^{5-2} = x^3 \)

Front

What happens when you divide powers with the same base?

Back

You subtract the exponents.

Front

Simplify: \( \frac{y^8}{y^3} \)

Back

\( y^{8-3} = y^5 \)

Front

What is the result of \( a^0 \)?

Back

Any non-zero number raised to the power of zero is 1: \( a^0 = 1 \).

Front

Simplify: \( \frac{z^6}{z^6} \)

Back

\( z^{6-6} = z^0 = 1 \)

Front

What is the Power of a Power Property?

Back

The Power of a Power Property states that when raising a power to another power, you multiply the exponents: \( (a^m)^n = a^{m \cdot n} \).

Front

Simplify: \( \left( x^3 \right)^4 \)

Back

\( x^{3 \cdot 4} = x^{12} \)

Front

What is the Power of a Product Property?

Back

The Power of a Product Property states that when raising a product to a power, you apply the exponent to each factor: \( (ab)^n = a^n b^n \).

Front

Simplify: \( \left( 2xy \right)^3 \)

Back

\( 2^3 x^3 y^3 = 8x^3y^3 \)