Algebra 1 Exponents Radicals Quiz – Free PDF

Contents

This algebra 1 exponents radicals quiz asks 10 multiple-choice questions on exponent rules, radicals and rational exponents, and each answer comes with a short explanation.

Ten multiple-choice questions check integer exponent rules, rational exponents and simplified radicals. Choose the one correct answer, then read the explanation to see the typical mistake. Several questions include a figure.

Algebra 1Common Core: N-RN.A.1 · N-RN.A.2

🎯 Exponent Rules, Radicals and Rational Exponents – Algebra 1 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

What is \(x^{3}\cdot x^{4}\)?

A \(x^{12}\)

B \(x^{7}\)

C \(2x^{7}\)

D \(x^{1}\)

Question 2

What is the value of \(2^{-3}\)?

A \(\frac{1}{8}\)

B \(-8\)

C \(-6\)

D \(\frac{1}{6}\)

Question 3

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

A \(9x^{6}\)

B \(27x^{5}\)

C \(27x^{6}\)

D \(3x^{6}\)

Question 4

What is \(125^{1/3}\)?

A \(5\)

B \(25\)

C \(375\)

D \(\frac{1}{5}\)

Question 5

The figure shows how to read \(8^{2/3}\). What is its value?

Denominator = root, numerator = power.

A \(\frac{16}{3}\)

B \(4\)

C \(16\)

D \(2\)

Question 6

Which expression equals \(\sqrt{72}\) in simplest form?

Pull out the largest perfect square.

A \(36\sqrt{2}\)

B \(6\sqrt{3}\)

C \(12\sqrt{6}\)

D \(6\sqrt{2}\)

Question 7

Which is equal to \(\sqrt[3]{x^{2}}\)?

A \(x^{3/2}\)

B \(x^{-2/3}\)

C \(x^{2/3}\)

D \(x^{6}\)

Question 8

Which equation matches the curve that passes through (4, 2) and (9, 3)?

A curve through (4, 2) and (9, 3).

A \(y=x^{2}\)

B \(y=\frac{x}{2}\)

C \(y=x^{-1/2}\)

D \(y=x^{1/2}\)

Question 9

A square patio has area 20 square feet. What is the side length?

Area 20 square feet.

A \(2\sqrt{5}\text{ ft}\)

B \(4\sqrt{5}\text{ ft}\)

C \(5\sqrt{2}\text{ ft}\)

D \(10\text{ ft}\)

Question 10

Simplify \(\dfrac{x^{8}}{x^{-2}}\).

A \(x^{6}\)

B \(x^{-6}\)

C \(x^{-16}\)

D \(x^{10}\)

🎉 Quiz complete!

0 / 10

How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Product rule: \(x^{m}\cdot x^{n}=x^{m+n}\); quotient rule: subtract the exponents.
Power of a power: multiply the exponents, \((x^{m})^{n}=x^{mn}\).
\(x^{0}=1\) and \(x^{-n}=\frac{1}{x^{n}}\) for \(x\neq 0\).
\(x^{m/n}=(\sqrt[n]{x})^{m}\): root in the denominator, power in the numerator.
Simplify a square root by pulling out the largest perfect square factor.