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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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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 is (2×103)(4×102)(2\times10^3)(4\times10^2)?

Please select an answer first.

Correct answer: A

The correct answer is 8×1058\times10^5.

  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: Multiply coefficients and add exponents: (2⋅4)×103+2=8×105(2\cdot4)\times10^{3+2}=8\times10^5.
  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.

Multiply coefficients and add exponents: (2⋅4)×103+2=8×105(2\cdot4)\times10^{3+2}=8\times10^5.

2. QuestionMultiple choice

What is 6×1072×103\frac{6\times10^7}{2\times10^3}?

Please select an answer first.

Correct answer: B

The correct answer is 3×1043\times10^4.

  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: Divide coefficients and subtract exponents: 62×107−3=3×104\frac{6}{2}\times10^{7-3}=3\times10^4.
  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.

Divide coefficients and subtract exponents: 62×107−3=3×104\frac{6}{2}\times10^{7-3}=3\times10^4.

3. QuestionMultiple choice

What is (3×104)+(2×104)(3\times10^4)+(2\times10^4)?

Please select an answer first.

Correct answer: C

The correct answer is 5×1045\times10^4.

  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: The powers of 10 match, so add the coefficients: (3+2)×104=5×104(3+2)\times10^4=5\times10^4.
  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.

The powers of 10 match, so add the coefficients: (3+2)×104=5×104(3+2)\times10^4=5\times10^4.

4. QuestionMultiple choice

What is (7.5×106)+(2.5×105)(7.5\times10^6)+(2.5\times10^5) in scientific notation?

Please select an answer first.

Correct answer: D

The correct answer is 7.75×1067.75\times10^6.

  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: Rewrite the second term as 0.25×1060.25\times10^6, then add: 7.5×106+0.25×106=7.75×1067.5\times10^6+0.25\times10^6=7.75\times10^6.
  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.

Rewrite the second term as 0.25×1060.25\times10^6, then add: 7.5×106+0.25×106=7.75×1067.5\times10^6+0.25\times10^6=7.75\times10^6.

5. QuestionMultiple choice

What is (5×103)(2×10−2)(5\times10^3)(2\times10^{-2})?

Please select an answer first.

Correct answer: A

The correct answer is 1×1021\times10^2.

  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: Multiply coefficients and add exponents: 10×103−2=10×101=1×10210\times10^{3-2}=10\times10^1=1\times10^2.
  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.

Multiply coefficients and add exponents: 10×103−2=10×101=1×10210\times10^{3-2}=10\times10^1=1\times10^2.

6. QuestionMultiple choice

What is 9×10−43×10−2\frac{9\times10^{-4}}{3\times10^{-2}}?

Please select an answer first.

Correct answer: B

The correct answer is 3×10−23\times10^{-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: Divide coefficients and subtract exponents: 3×10−4−(−2)=3×10−23\times10^{-4-(-2)}=3\times10^{-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.

Divide coefficients and subtract exponents: 3×10−4−(−2)=3×10−23\times10^{-4-(-2)}=3\times10^{-2}.

7. QuestionMultiple choice

Which is the scientific notation for 0.000000560.00000056?

Please select an answer first.

Correct answer: C

The correct answer is 5.6×10−75.6\times10^{-7}.

  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: Move the decimal seven places right to make 5.6, so the exponent is -7.
  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.

Move the decimal seven places right to make 5.6, so the exponent is -7.

8. QuestionMultiple choice

Which is the scientific notation for 72,000,00072,000,000?

Please select an answer first.

Correct answer: D

The correct answer is 7.2×1077.2\times10^7.

  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: Move the decimal seven places left: 72,000,000=7.2×10772,000,000=7.2\times10^7.
  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.

Move the decimal seven places left: 72,000,000=7.2×10772,000,000=7.2\times10^7.

9. QuestionMultiple choice

Which value is closest to (3.1×102)(2.9×103)(3.1\times10^2)(2.9\times10^3)?

Please select an answer first.

Correct answer: A

The correct answer is 9×1059\times10^5.

  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 coefficients are close to 3⋅3=93\cdot3=9 and the powers give 102+3=10510^{2+3}=10^5, so the product is close to 9×1059\times10^5.
  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 coefficients are close to 3⋅3=93\cdot3=9 and the powers give 102+3=10510^{2+3}=10^5, so the product is close to 9×1059\times10^5.

10. QuestionMultiple choice

Why must the coefficient be adjusted after some scientific-notation operations?

Please select an answer first.

Correct answer: B

The correct answer is To keep the coefficient at least 1 and less than 10..

  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 example, 12×104=1.2×10512\times10^4=1.2\times10^5 is standard scientific notation.
  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 example, 12×104=1.2×10512\times10^4=1.2\times10^5 is standard scientific notation.

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