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Exponents roots practice questions

25 questions from the electrical apprenticeship aptitude practice test.

Exponents roots practice test

10 questions, graded as you go, with the reason for every answer. No sign-up.

What this covers

Sample questions

Which of these powers has the greatest value?

  1. 3^3
  2. 5^2
  3. 10^1
  4. 2^5
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D. 2^5

2^5 = 32, 3^3 = 27, 5^2 = 25 and 10^1 = 10, so 2^5 is the largest. A bigger base does not guarantee a bigger value; the exponent matters as much.

Reference: Comparing powers

Simplify: x^9 ÷ x^3

  1. x^6
  2. x^3
  3. x^12
  4. x^27
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A. x^6

When powers of the same base are divided, subtract the exponents: 9 − 3 = 6. Dividing the exponents to get x^3 is the tempting error.

Reference: Quotient rule for exponents

Simplify: (x^4)^3

  1. x^7
  2. x^64
  3. x^12
  4. 3x^4
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C. x^12

A power raised to a power multiplies the exponents: 4 × 3 = 12. Adding them to get x^7 is the rule for multiplying x^4 by x^3, which is a different operation.

Reference: Power rule for exponents

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