This algebra 1 exponents radicals test checks exponent rules, radicals and rational exponents in 45 minutes, with 9 questions for a total of 20 points.
This test covers Common Core standards N-RN.A.1 and N-RN.A.2: integer exponent rules, rational exponents, radicals and simplifying square roots. Nine questions are worth 20 points in total. Show your work, write answers in simplest form, and use a calculator only for decimal approximations.
- Grade: Algebra 1
- Chapter: Exponent Rules, Radicals and Rational Exponents
- Common Core: N-RN.A.1, N-RN.A.2
- Time: 45 minutes
- Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 2 pts; Question 5: 2 pts; Question 6: 3 pts; Question 7: 2 pts; Question 8: 3 pts; Question 9: 2 pts)
Algebra 1 Exponents Radicals Test: questions 1–5
Question 1: Powers of 3 (2 points)
The table shows powers of 3.
- Find \(3^{0}\). (1 point)
- Find \(3^{-2}\). (1 point)
Question 2: Monomial products and quotients (2 points)
Simplify. Assume no variable equals 0.
- \((4x^{3}y)(-2x^{2}y^{4})\) (1 point)
- \(\dfrac{18a^{7}b^{2}}{6a^{2}b}\) (1 point)
Question 3: Combining power rules (2 points)
Simplify and write each answer with positive exponents.
- \((x^{4})^{-2}\cdot x^{11}\) (1 point)
- \((2x^{-2}y)^{3}\) (1 point)
Question 4: Rational exponent values (2 points)
Evaluate.
- \(25^{3/2}\) (1 point)
- \(32^{-2/5}\) (1 point)
Question 5: Radical and exponent forms (2 points)
Rewrite each expression in the other form.
- Write \(\sqrt[3]{x^{4}}\) with a rational exponent. (1 point)
- Write \(y^{5/2}\) as a radical. (1 point)
Algebra 1 Exponents Radicals Test: questions 6–9
Question 6: Simplify square roots (3 points)
Write each expression in simplest form. Assume \(x>0\).
- \(\sqrt{45}\) (1 point)
- \(\sqrt{80}\) (1 point)
- \(\sqrt{12x^{5}}\) (1 point)
Question 7: Exponent rules with fractions (2 points)
Simplify. Assume \(x>0\).
- \((x^{3/4})^{8}\) (1 point)
- \(\dfrac{x^{7/3}}{x^{1/3}}\) (1 point)
Question 8: Graph of a rational power (3 points)
The graph shows \(y=x^{1/2}\).
- Find \(y\) when \(x=16\). (1 point)
- Write the equation using a radical. (1 point)
- Does the point (25, 5) lie on the graph? Show why. (1 point)
Question 9: Square frame (2 points)
A square picture frame has an area of 150 square inches. Find its side length in simplest radical form (1 point) and to the nearest tenth of an inch (1 point).
How to use this algebra 1 exponents radicals test
Take this algebra 1 exponents radicals test without notes, then grade it with the test answer key out of 20 points.
See every chapter on the Algebra 1 math page.