Properties of Exponents with Radicals & Rational Exponents

Front

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

Back

This property allows us to express negative exponents as fractions.

Front

Simplify the expression: \( (t^{-6})^{-5} \)

Back

\( t^{30} \)

Front

What is the equivalent expression in exponential form for \( 224^{\frac{1}{5}}r^{\frac{1}{35}} \)?

Back

\( (224r^7)^{\frac{1}{5}} \)

Front

Simplify the expression: \( \frac{12x^9y^4z^2}{24x^3y^4z^6} \)

Back

\( \frac{x^6}{2z^4} \)

Front

What is the product of \( 3x^2 \cdot x^2 \)?

Back

\( 3x^4 \)

Front

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

Back

This property allows us to add the exponents when multiplying like bases.

Front

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

Back

This property allows us to subtract the exponents when dividing like bases.

Front

Simplify the expression: \( (a^4b)^2(a^3b^2)^4 \)

Back

\( a^{20}b^{10} \)

Front

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

Back

This property allows us to multiply the exponents when raising a power to another power.

Front

What is the value of \( 2^{-3} \)?

Back

\( \frac{1}{8} \)