Algebra 1 Exponent Rules and Radicals Test with Point Values (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.
Time and points
- 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]
- Evaluate \(2^{5} \cdot 2^{-2}\). (1 point)
- 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]
The square has area 98 square inches. Write its side length in simplest radical form.
Question 5 – Rational exponents [2 pts]
Evaluate each expression.
- \(64^{1/3}\) (1 point)
- \(9^{3/2}\) (1 point)
Question 6 – Radicals and exponents [2 pts]
- Write \(x^{3/4}\) as a radical. (1 point)
- Write \(\sqrt[5]{y^{2}}\) with a rational exponent. (1 point)
Question 7 – Rational or irrational [3 pts]
The number line shows \(\sqrt{11}\) and 3.
- Classify \(\sqrt{81}\) as rational or irrational. (1 point)
- Classify \(\sqrt{11}\) as rational or irrational. (1 point)
- Explain why \(3 + \sqrt{5}\) is irrational. (1 point)
Question 8 – Population model [3 pts]
A population is modeled by \(P = 50 \cdot 3^{t}\) where \(t\) is in hours.
- Find \(P(0)\). (1 point)
- Find \(P(4)\). (1 point)
- 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.
Key facts behind this exponent rules test
- 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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