Exponent Rules, Radicals and Rational Exponents: Algebra 1 Math Quiz – PDF Download
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
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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!
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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.
