Pre-Algebra Practice Test: Exponents and Square Roots
- Exponents and Square Roots
- 10 questions
- 12 minutes
This test covers evaluating powers, exponent rules, perfect squares and estimating square roots. Tip: an exponent tells how many times the base is used as a factor, so 5³ = 5 × 5 × 5, not 5 × 3.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
What is 53?
Correct answer: C
5³ = 5 × 5 × 5 = 125. The answer 15 multiplies the base by the exponent.
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Question 2
What is (−2)4?
Correct answer: A
The base −2 is used four times: (−2)(−2)(−2)(−2) = 16. An even number of negative factors gives a positive result.
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Question 3
What is 81 + 16?
Correct answer: D
√81 = 9 and √16 = 4, so the sum is 13. Square roots cannot be added by adding the numbers under the root sign first.
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Question 4
What is 100 + 22?
Correct answer: B
Any nonzero number to the power 0 equals 1, so 1 + 4 = 5. Treating 10⁰ as 0 gives 4.
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Question 5
Which is equal to 34 × 32?
Correct answer: A
When multiplying powers with the same base, keep the base and add the exponents: 4 + 2 = 6.
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Question 6
Between which two consecutive whole numbers does 50 lie?
Correct answer: C
7² = 49 and 8² = 64, and 50 is between them, so √50 is between 7 and 8 (very close to 7).
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Question 7
Which number is equal to 25?
Correct answer: B
2⁵ = 2 × 2 × 2 × 2 × 2 = 32. The answer 64 is 2⁶.
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Question 8
A square garden has an area of 144 square feet. How long is each side?
Correct answer: D
The side of a square is the square root of its area: √144 = 12 feet. Dividing 144 by 4 gives 36, which mixes up area and perimeter.
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Question 9
What is 4 × 103 + 6 × 10?
Correct answer: C
4 × 1,000 = 4,000 and 6 × 10 = 60, so the sum is 4,060.
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Question 10
What is 2 × 32?
Correct answer: D
The exponent applies only to 3: 3² = 9, then 2 × 9 = 18. Squaring 2 × 3 first gives 36.
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