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Exponents and Scientific Notation Practice Tests

These Grade 8 Math practice tests cover exponent rules, zero and negative exponents, powers of 10, scientific notation, operations, comparisons, and real-world measurements.

Skills covered

  • Evaluating powers and applying product, quotient, power-of-a-power, and power-of-a-product rules
  • Interpreting zero and negative exponents and writing reciprocal forms
  • Converting between standard form and scientific notation
  • Multiplying, dividing, adding, and comparing numbers in scientific notation
  • Using powers of 10 to describe very large and very small measurements

How to use these practice tests

Identify the base and exponent first. For scientific notation, count decimal places and confirm that the coefficient is at least 1 and less than 10. Keep units when solving real-world problems.

For more Grade 8 Math practice, return to the Grade 8 Math category.

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1. Test

Grade 8 Exponents and Scientific Notation Practice Tests

Practice Grade 8 Math questions about exponent rules, powers of ten, negative exponents, scientific notation, operations, comparisons, and real-world scale.

Choose the best answer for each question. Write powers and scientific notation carefully, then review the explanation after submitting your answers.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What does the exponent in 535^3 represent?

Please select an answer first.

Correct answer: A

The correct answer is The number of times 5 is used as a factor.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: 53=5⋅5⋅55^3=5\cdot5\cdot5, so the exponent 3 tells how many equal factors appear.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

53=5⋅5⋅55^3=5\cdot5\cdot5, so the exponent 3 tells how many equal factors appear.

2. QuestionMultiple choice

What is the value of 242^4?

Please select an answer first.

Correct answer: B

The correct answer is 1616.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: 24=2⋅2⋅2⋅2=162^4=2\cdot2\cdot2\cdot2=16.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

24=2⋅2⋅2⋅2=162^4=2\cdot2\cdot2\cdot2=16.

3. QuestionMultiple choice

What is the value of 707^0?

Please select an answer first.

Correct answer: C

The correct answer is 11.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: Any nonzero number raised to the zero power equals 1.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

Any nonzero number raised to the zero power equals 1.

4. QuestionMultiple choice

What is the value of 10−210^{-2}?

Please select an answer first.

Correct answer: D

The correct answer is 0.010.01.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: 10−2=1102=1100=0.0110^{-2}=\frac{1}{10^2}=\frac{1}{100}=0.01.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

10−2=1102=1100=0.0110^{-2}=\frac{1}{10^2}=\frac{1}{100}=0.01.

5. QuestionMultiple choice

Which expression is equivalent to 32⋅343^2\cdot3^4?

Please select an answer first.

Correct answer: A

The correct answer is 363^6.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: When multiplying powers with the same base, add the exponents: 32⋅34=32+4=363^2\cdot3^4=3^{2+4}=3^6.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

When multiplying powers with the same base, add the exponents: 32⋅34=32+4=363^2\cdot3^4=3^{2+4}=3^6.

6. QuestionMultiple choice

Which expression is equivalent to 5753\frac{5^7}{5^3}?

Please select an answer first.

Correct answer: B

The correct answer is 545^4.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: When dividing powers with the same nonzero base, subtract the exponents: 57−3=545^{7-3}=5^4.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

When dividing powers with the same nonzero base, subtract the exponents: 57−3=545^{7-3}=5^4.

7. QuestionMultiple choice

Which expression is equivalent to (23)4(2^3)^4?

Please select an answer first.

Correct answer: C

The correct answer is 2122^{12}.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: For a power raised to a power, multiply the exponents: (23)4=23⋅4=212(2^3)^4=2^{3\cdot4}=2^{12}.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

For a power raised to a power, multiply the exponents: (23)4=23⋅4=212(2^3)^4=2^{3\cdot4}=2^{12}.

8. QuestionMultiple choice

Which expression is equivalent to (3⋅5)2(3\cdot5)^2?

Please select an answer first.

Correct answer: D

The correct answer is 32⋅523^2\cdot5^2.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: The power of a product applies to each factor: (3⋅5)2=32⋅52(3\cdot5)^2=3^2\cdot5^2.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

The power of a product applies to each factor: (3⋅5)2=32⋅52(3\cdot5)^2=3^2\cdot5^2.

9. QuestionMultiple choice

What is the value of 919^1?

Please select an answer first.

Correct answer: A

The correct answer is 99.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: Any number raised to the first power remains unchanged: 91=99^1=9.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

Any number raised to the first power remains unchanged: 91=99^1=9.

10. QuestionMultiple choice

Which operation should be completed first in 2+322+3^2?

Please select an answer first.

Correct answer: B

The correct answer is The exponent.

  1. Identify the exponent or notation task: Determine whether the question asks you to evaluate, simplify, convert, compare, or operate with powers and scientific notation.
  2. Apply the exponent rule: Order of operations requires evaluating the exponent before addition, so 2+32=2+9=112+3^2=2+9=11.
  3. Check place value and scale: Count the powers of 10, verify the decimal placement, and make sure the coefficient in scientific notation is at least 1 and less than 10.

Order of operations requires evaluating the exponent before addition, so 2+32=2+9=112+3^2=2+9=11.

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