Algebra 1 Exponent Rules and Radicals Test with Point Values (PDF)

Algebra 1 math test: Exponent Rules and Radicals – Maths PDF


This exponent rules test for Algebra 1 covers exponent rules and radicals (Common Core N-RN.A.1, N-RN.A.2, N-RN.B.3), with a free PDF to print.

This test checks exponent rules and radicals for Common Core N-RN.A.1, N-RN.A.2, and N-RN.B.3. It has 9 questions worth 20 points in all, and you have 45 minutes. Write clear steps, because points are awarded for method as well as for the final answer. Leave a few minutes to review.

Time and points

About this test
  • Grade: Algebra 1
  • Chapter: Exponent Rules and Radicals
  • Standards: N-RN.A.1, N-RN.A.2, N-RN.B.3
  • Time: 45 minutes
  • Total: 20 points

Exponent rules test: questions

Question 1 – Evaluate with exponent rules [2 pts]

  1. Evaluate \(2^{5} \cdot 2^{-2}\). (1 point)
  2. Evaluate \(\frac{(3^{2})^{3}}{3^{4}}\). (1 point)

Question 2 – Power of a product [2 pts]

Simplify \((4x^{3}y^{2})^{2}\).

Question 3 – Negative exponents [2 pts]

Simplify \(\frac{x^{-3}y^{4}}{x^{2}y}\) and write the answer with positive exponents.

Question 4 – Simplify a radical [2 pts]

√98√98Area 98
A square with area 98.

The square has area 98 square inches. Write its side length in simplest radical form.

Question 5 – Rational exponents [2 pts]

Evaluate each expression.

  1. \(64^{1/3}\) (1 point)
  2. \(9^{3/2}\) (1 point)

Question 6 – Radicals and exponents [2 pts]

  1. Write \(x^{3/4}\) as a radical. (1 point)
  2. Write \(\sqrt[5]{y^{2}}\) with a rational exponent. (1 point)

Question 7 – Rational or irrational [3 pts]

01234√11√81 / 3
Number line for question 7.

The number line shows \(\sqrt{11}\) and 3.

  1. Classify \(\sqrt{81}\) as rational or irrational. (1 point)
  2. Classify \(\sqrt{11}\) as rational or irrational. (1 point)
  3. Explain why \(3 + \sqrt{5}\) is irrational. (1 point)

Question 8 – Population model [3 pts]

Hours t0123P501504501350
Population values of P = 50 · 3^t.

A population is modeled by \(P = 50 \cdot 3^{t}\) where \(t\) is in hours.

  1. Find \(P(0)\). (1 point)
  2. Find \(P(4)\). (1 point)
  3. Find \(t\) when \(P = 1350\). (1 point)

Question 9 – Find the error [2 pts]

A student wrote \((2x)^{3} = 2x^{3}\). Explain the error and give the correct result.

See the solutions: Exponent Rules and Radicals test solutions

Key facts behind this exponent rules test

Key facts
  • Product rule: aᵐ · aⁿ = aᵐ⁺ⁿ; quotient rule: aᵐ / aⁿ = aᵐ⁻ⁿ.
  • Power rule: (aᵐ)ⁿ = aᵐⁿ.
  • a⁰ = 1 and a⁻ⁿ = 1/aⁿ for a ≠ 0.
  • a^(1/2) = √a, and a^(m/n) is the n-th root of a raised to the m.
  • A rational plus an irrational number is irrational.

How to use this exponent rules test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 1 chapters: Algebra 1 math.

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Algebra 1 Exponent Rules and Radicals Test with Point Values

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