Grade 9 · Algebra & functions

Rational exponents practice

Rational exponents is a grade 9 math skill aligned to Common Core standard HSN.RN.A.1: explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 15 rational exponents problems our math games drill.

CCSS HSN.RN.A.115 questions in the bank

Sample questions

Try 8 for free

Question 1easy

Evaluate $27^{-1/3}$ .

$27^{-1/3} = \dfrac{1}{27^{1/3}} = \dfrac{1}{3}$ .

Question 2easy

Simplify: $16^{1/2}$ .

$16^{1/2} = \sqrt{16} = 4$ .

Question 3easy

Simplify: $27^{2/3}$ .

$27^{2/3} = (\sqrt[3]{27})^2 = 3^2 = 9$ .

Question 4easy

Write $\sqrt[3]{x^2}$ as $x^{a/b}$ in lowest terms. What is $a$ ?

$\sqrt[3]{x^2} = x^{2/3}$ , so $a = 2$ .

Question 5easy

Simplify: $25^{1/2}$ .

$25^{1/2} = \sqrt{25} = 5$ .

Question 6easy

Simplify: $32^{2/5}$ .

$32^{2/5} = (\sqrt[5]{32})^2 = 2^2 = 4$ .

Question 7easy

Write $\sqrt[5]{x^3}$ as $x^{a/b}$ in lowest terms. What is $b$ ?

$\sqrt[5]{x^3} = x^{3/5}$ , so $b = 5$ .

Question 8easy

Evaluate $49^{1/2}$ .

$49^{1/2} = \sqrt{49} = 7$ .

Tests that cover rational exponents:

NAEP SBAC SAT NC EOG/EOC VTCAP

More Grade 9 skills:

Rational equation solving (SAT)Slope-intercept intercepts Radical to exponent conversions Slope-point line equations Quadratic minimum x-value Systems of equations Quadratic formula Quadratic distinct real solutions count All Grade 9 practice →

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