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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

Which expression is equivalent to x3⋅x2x^3\cdot x^2?

Please select an answer first.

Correct answer: A

The correct answer is x5x^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: For the same base, add exponents: x3⋅x2=x3+2=x5x^3\cdot x^2=x^{3+2}=x^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.

For the same base, add exponents: x3⋅x2=x3+2=x5x^3\cdot x^2=x^{3+2}=x^5.

2. QuestionMultiple choice

Which expression is equivalent to a8a5\frac{a^8}{a^5}?

Please select an answer first.

Correct answer: B

The correct answer is a3a^3.

  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 the same nonzero base, subtract exponents: a8−5=a3a^{8-5}=a^3.
  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 the same nonzero base, subtract exponents: a8−5=a3a^{8-5}=a^3.

3. QuestionMultiple choice

Which expression is equivalent to (m2n3)2(m^2n^3)^2?

Please select an answer first.

Correct answer: C

The correct answer is m4n6m^4n^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: Multiply each exponent by the outside exponent: (m2n3)2=m2⋅2n3⋅2=m4n6(m^2n^3)^2=m^{2\cdot2}n^{3\cdot2}=m^4n^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.

Multiply each exponent by the outside exponent: (m2n3)2=m2⋅2n3⋅2=m4n6(m^2n^3)^2=m^{2\cdot2}n^{3\cdot2}=m^4n^6.

4. QuestionMultiple choice

Which expression is equivalent to 1y4\frac{1}{y^4}?

Please select an answer first.

Correct answer: D

The correct answer is y−4y^{-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: A negative exponent represents a reciprocal: y−4=1y4y^{-4}=\frac{1}{y^4} for nonzero yy.
  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.

A negative exponent represents a reciprocal: y−4=1y4y^{-4}=\frac{1}{y^4} for nonzero yy.

5. QuestionMultiple choice

What is the value of 2−32^{-3}?

Please select an answer first.

Correct answer: A

The correct answer is 18\frac{1}{8}.

  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: 2−3=123=182^{-3}=\frac{1}{2^3}=\frac{1}{8}.
  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.

2−3=123=182^{-3}=\frac{1}{2^3}=\frac{1}{8}.

6. QuestionMultiple choice

Which expression is equivalent to (23)2\left(\frac{2}{3}\right)^2?

Please select an answer first.

Correct answer: B

The correct answer is 49\frac{4}{9}.

  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: Apply the exponent to the numerator and denominator: (23)2=2232=49\left(\frac{2}{3}\right)^2=\frac{2^2}{3^2}=\frac{4}{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.

Apply the exponent to the numerator and denominator: (23)2=2232=49\left(\frac{2}{3}\right)^2=\frac{2^2}{3^2}=\frac{4}{9}.

7. QuestionMultiple choice

Which expression is equal to 103⋅10−510^3\cdot10^{-5}?

Please select an answer first.

Correct answer: C

The correct answer is 10−210^{-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: Add the exponents: 103+(−5)=10−210^{3+(-5)}=10^{-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.

Add the exponents: 103+(−5)=10−210^{3+(-5)}=10^{-2}.

8. QuestionMultiple choice

Which statement about 4.2×1004.2\times10^0 is true?

Please select an answer first.

Correct answer: D

The correct answer is 4.2×100=4.24.2\times10^0=4.2.

  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: Since 100=110^0=1, multiplying 4.2 by 10010^0 leaves 4.2 unchanged.
  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.

Since 100=110^0=1, multiplying 4.2 by 10010^0 leaves 4.2 unchanged.

9. QuestionMultiple choice

Which number has the greatest magnitude?

Please select an answer first.

Correct answer: A

The correct answer is 8×1068\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: The greatest power of 10 is 10610^6, and its coefficient is also larger than the comparable 7×1067\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.

The greatest power of 10 is 10610^6, and its coefficient is also larger than the comparable 7×1067\times10^6.

10. QuestionMultiple choice

What is a useful check after simplifying an exponent expression?

Please select an answer first.

Correct answer: B

The correct answer is Substitute a simple nonzero value and compare the original and simplified expressions..

  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: A test value can reveal an incorrect exponent operation while keeping the algebraic rule transparent.
  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.

A test value can reveal an incorrect exponent operation while keeping the algebraic rule transparent.

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