Exponent Properties

Front

What is the Quotient of Powers Rule?

Back

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

Front

Simplify: \( \frac{9^9}{9^4} \)

Back

Using the Quotient of Powers Rule: \( 9^{9-4} = 9^5 \).

Front

What is the Power of a Power Rule?

Back

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

Front

Simplify: \( ((-2r)^3)^2 \)

Back

Using the Power of a Power Rule: \( (-2r)^{3 \cdot 2} = (-2r)^6 = 64r^6 \).

Front

What is the Power of a Product Rule?

Back

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

Front

Simplify: \( (-3x^4y^5)^2 \)

Back

Using the Power of a Product Rule: \( (-3)^2 (x^4)^2 (y^5)^2 = 9x^8y^{10} \).

Front

What is the Power of a Quotient Rule?

Back

The Power of a Quotient Rule states that when raising a quotient to a power, you apply the exponent to both the numerator and the denominator: \( \left( \frac{a}{b} \right)^n = \frac{a^n}{b^n} \).

Front

Simplify: \( \left( \frac{3x^2y^3}{6x^5} \right)^3 \)

Back

Using the Power of a Quotient Rule: \( \frac{(3x^2y^3)^3}{(6x^5)^3} = \frac{27x^6y^9}{216x^{15}} = \frac{27y^9}{216x^9} \).

Front

What does it mean to simplify an expression with exponents?

Back

To simplify an expression with exponents means to rewrite it in a more compact form, often by combining like terms and using exponent rules to eliminate negative exponents.

Front

What is a negative exponent?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: \( a^{-n} = \frac{1}{a^n} \).