Grade 9 · Algebra & functions

Radical to exponent conversions practice

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
Sample questions

Try 8 for free

Question 1easy

Which expression is equivalent to a8b124\sqrt[4]{a^8 b^{12}}, where aa and bb are positive?

Divide each exponent by 44: a8/4b12/4=a2b3a^{8/4} b^{12/4} = a^2 b^3.

Question 2easy

Which expression is equivalent to m10n155\sqrt[5]{m^{10} n^{15}}, where mm and nn are positive?

Divide each exponent by 55: m10/5n15/5=m2n3m^{10/5} n^{15/5} = m^2 n^3.

Question 3easy

Which expression is equivalent to x10y8\sqrt{x^{10} y^8}, where xx and yy are positive?

A square root divides each exponent by 22: x10/2y8/2=x5y4x^{10/2} y^{8/2} = x^5 y^4.

Question 4medium

Which expression is equivalent to x9y97\sqrt[7]{x^9 y^9}, where xx and yy are positive?

A seventh root applies the exponent 17\dfrac{1}{7} to the product: (x9y9)1/7=x9/7y9/7(x^9 y^9)^{1/7} = x^{9/7} y^{9/7}.

Question 5medium

Which expression is equivalent to r21s14t77\sqrt[7]{r^{21} s^{14} t^7}, where rr, ss, and tt are positive?

Divide each exponent by 77: r21/7s14/7t7/7=r3s2tr^{21/7} s^{14/7} t^{7/7} = r^3 s^2 t.

Question 6medium

Which expression is equivalent to u15v9w63\sqrt[3]{u^{15} v^9 w^6}, where uu, vv, and ww are positive?

Divide each exponent by 33: u15/3v9/3w6/3=u5v3w2u^{15/3} v^{9/3} w^{6/3} = u^5 v^3 w^2.

Question 7hard

Which expression is equivalent to a5b64\sqrt[4]{a^5 b^6}, where aa and bb are positive?

Divide each exponent by 44: a5/4b6/4=a5/4b3/2a^{5/4} b^{6/4} = a^{5/4} b^{3/2}.

Question 8hard

Which expression is equivalent to x8y125\sqrt[5]{x^8 y^{12}}, where xx and yy are positive?

Divide each exponent by 55: x8/5y12/5x^{8/5} y^{12/5}.

Drill it inside a game.

The free placement test finds your level, then every match serves radical to exponent conversions questions at exactly the right difficulty.