Radical to exponent conversions Practice Questions (Grade 9)

Radical to exponent conversions. Game on.

Radical to exponent conversions is a grade 9 math skill aligned to Common Core standard HSN.RN.A.2: rewrite expressions involving radicals and rational exponents using the properties of exponents. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 radical to exponent conversions problems our math games drill.

CCSS HSN.RN.A.210 questions in the bank

8 plays. No signup.

Warm-upeasy

If $\Large a$ and $\Large b$ are positive, which expression is equivalent to $\Large \sqrt[4]{a^8 b^{12}}$ ?

Divide each exponent by $\Large 4$ : $\Large a^{\tfrac{8}{4}} b^{\tfrac{12}{4}} = a^2 b^3$ .

Mid-gameeasy

If $\Large m$ and $\Large n$ are positive, which expression is equivalent to $\Large \sqrt[5]{m^{10} n^{15}}$ ?

Divide each exponent by $\Large 5$ : $\Large m^{\tfrac{10}{5}} n^{\tfrac{15}{5}} = m^2 n^3$ .

Mid-gameeasy

If $\Large x$ and $\Large y$ are positive, which expression is equivalent to $\Large \sqrt{x^{10} y^8}$ ?

A square root divides each exponent by $\Large 2$ : $\Large x^{\tfrac{10}{2}} y^{\tfrac{8}{2}} = x^5 y^4$ .

Mid-gamemedium

If $\Large p$ and $\Large q$ are positive, which expression is equivalent to $\Large \sqrt[6]{p^{18} q^{12}}$ ?

Divide each exponent by $\Large 6$ : $\Large p^{\tfrac{18}{6}} q^{\tfrac{12}{6}} = p^3 q^2$ .

Mid-gamemedium

If $\Large r$ , $\Large s$ , and $\Large t$ are positive, which expression is equivalent to $\Large \sqrt[7]{r^{21} s^{14} t^7}$ ?

Divide each exponent by $\Large 7$ : $\Large r^{\tfrac{21}{7}} s^{\tfrac{14}{7}} t^{\tfrac{7}{7}} = r^3 s^2 t$ .

Mid-gamemedium

If $\Large u$ , $\Large v$ , and $\Large w$ are positive, which expression is equivalent to $\Large \sqrt[3]{u^{15} v^9 w^6}$ ?

Divide each exponent by $\Large 3$ : $\Large u^{\tfrac{15}{3}} v^{\tfrac{9}{3}} w^{\tfrac{6}{3}} = u^5 v^3 w^2$ .

Mid-gamehard

If $\Large a$ and $\Large b$ are positive, which expression is equivalent to $\Large \sqrt[4]{a^5 b^6}$ ?

Divide each exponent by $\Large 4$ : $\Large a^{\tfrac{5}{4}} b^{\tfrac{6}{4}} = a^{\tfrac{5}{4}} b^{\tfrac{3}{2}}$ .

Buzzer beaterhard

If $\Large x$ and $\Large y$ are positive, which expression is equivalent to $\Large \sqrt[5]{x^8 y^{12}}$ ?

Divide each exponent by $\Large 5$ : $\Large x^{\tfrac{8}{5}} y^{\tfrac{12}{5}}$ .

Radical to exponent conversions. Game on.

8 plays. No signup.

2 more. Played, not assigned.

Drill it inside a game.