Exponents Practice Questions

Use these exponents practice questions to review scientific notation, exponent rules, zero and negative exponents, fractional exponents, and expressions containing multiple variables. After answering each question, open the explanation to compare your work with the step-by-step solution.

Topics Covered

  • Writing numbers in scientific notation
  • Converting scientific notation to standard notation
  • The product rule for exponents
  • The quotient rule for exponents
  • The power-of-a-power rule
  • The zero-exponent rule
  • Negative exponents
  • Fractional exponents
  • Simplifying multivariable exponential expressions

Sample Questions

1. Write 0.000064 in scientific notation.

  • A. 6.4 × 10−6
  • B. 6.4 × 10−5
  • C. 6.4 × 10−4
  • D. 64 × 10−5
  • E. 6.4 × 105
Show Answer for Question 1
Answer: B. 6.4 × 10−5

Move the decimal point five places to the right to obtain 6.4.

Because the original number is less than 1, the exponent is negative. Therefore, 0.000064 = 6.4 × 10−5.

2. Write 3.27 × 104 in standard notation.

  • A. 327
  • B. 3,270
  • C. 32,700
  • D. 327,000
  • E. 0.000327
Show Answer for Question 2
Answer: C. 32,700

A positive exponent of 4 means move the decimal point four places to the right.

3.27 × 104 = 32,700.

3. Simplify x5 · x3.

  • A. x8
  • B. x15
  • C. 2x8
  • D. x2
  • E. x5/3
Show Answer for Question 3
Answer: A. x8

When multiplying powers with the same base, add the exponents.

x5 · x3 = x5 + 3 = x8.

4. Simplify y4 ÷ y−2, assuming y ≠ 0.

  • A. y−8
  • B. y−2
  • C. y2
  • D. y6
  • E. y8
Show Answer for Question 4
Answer: D. y6

When dividing powers with the same base, subtract the exponent in the denominator from the exponent in the numerator.

y4 ÷ y−2 = y4 − (−2) = y6.

5. Simplify (2a3)2.

  • A. 2a5
  • B. 4a5
  • C. 4a6
  • D. 8a6
  • E. 2a6
Show Answer for Question 5
Answer: C. 4a6

Apply the outer exponent to both the coefficient and the variable factor.

(2a3)2 = 22(a3)2 = 4a6.

6. Simplify 7m0, assuming m ≠ 0.

  • A. 0
  • B. 1
  • C. 7
  • D. 7m
  • E. m7
Show Answer for Question 6
Answer: C. 7

Any nonzero base raised to the zero power equals 1.

7m0 = 7(1) = 7.

7. Rewrite 6p−3 using only positive exponents.

  • A. 6p3
  • B. −6p3
  • C. 6/p3
  • D. p3/6
  • E. 1/(6p3)
Show Answer for Question 7
Answer: C. 6/p3

A negative exponent indicates a reciprocal of the power.

p−3 = 1/p3, so 6p−3 = 6/p3.

8. Evaluate 811/2.

  • A. 3
  • B. 9
  • C. 27
  • D. 40.5
  • E. 81
Show Answer for Question 8
Answer: B. 9

An exponent of 1/2 represents the principal square root.

811/2 = √81 = 9.

9. Simplify (a4b−2)/(a−1b3) using only positive exponents.

  • A. a3b
  • B. a5b
  • C. a5/b5
  • D. b5/a5
  • E. a3/b
Show Answer for Question 9
Answer: C. a5/b5

Subtract exponents for each common base: a4 − (−1) = a5 and b−2 − 3 = b−5.

Rewrite the negative exponent with a positive exponent in the denominator: a5b−5 = a5/b5.

10. Simplify ((3x2y)2)/(9xy−1), assuming x ≠ 0 and y ≠ 0.

  • A. x2y
  • B. x3y3
  • C. 3x3y
  • D. 9x3y3
  • E. x4y2
Show Answer for Question 10
Answer: B. x3y3

First simplify the numerator: (3x2y)2 = 9x4y2.

Then divide coefficients and subtract exponents: (9x4y2)/(9xy−1) = x4 − 1y2 − (−1) = x3y3.

How to Use These Questions

Identify the rule required before simplifying. Add exponents when multiplying like bases, subtract exponents when dividing like bases, and multiply exponents when raising a power to another power.

Rewrite final answers with positive exponents unless the directions say otherwise. Remember that a zero exponent applies only to a nonzero base and that a fractional exponent can represent a root.

 

Last Updated: August 4, 2026