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Common Core Math8th GradeExpressions & Equations

8.EE.1: Properties of Integer Exponents

Also written as 8.EE.A.1 and CCSS.MATH.CONTENT.8.EE.A.1 · Cluster: Work with radicals and integer exponents.

Make 8.EE.1 ProblemsAll 28 8th Grade Math Standards

The Official Wording

Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3⁻⁵ = 3⁻³ = 1/3³ = 1/27.

Common Core State Standards, Grade 8, Expressions & Equations · Read it at the source · Checked October 14, 2026

What 8.EE.1 Means in Plain English

Eighth graders use the exponent rules and can say why they work: 7⁴ × 7² = 7⁶ because six 7s are multiplied, 7⁶ ÷ 7⁴ = 7², and (7²)³ = 7⁶. The pattern continues to 7⁰ = 1 and 7⁻² = 1/49, a reciprocal, not a negative number.

Every answer is a number, so students can check a rewrite by evaluating both forms. The rules power scientific notation next (8.EE.3, 8.EE.4), and in high school they stretch to fractional exponents, where 8 to the power one third is 2 (HSN-RN.1).

8.EE.1 I Can Statements

  • I can multiply and divide powers with the same base.
  • I can raise a power to a power by multiplying exponents.
  • I can rewrite a negative exponent as a fraction, like 3⁻² = 1/9.

8.EE.1 Worked Example

Three exponent rules in one expression, with negative exponents that cancel out to a positive power.

Problem

Write (2⁵ × 2⁻⁸) ÷ (2²)⁻³ as a single power of 2, then evaluate it.

Simplifying (2⁵ × 2⁻⁸) ÷ (2²)⁻³
  1. Multiplying powers with the same base adds the exponents, and adding -8 is the same as subtracting 8.2⁵ × 2⁻⁸ = 2⁻³, because 5 + (-8) = -3
  2. A power of a power multiplies the exponents: (2²)⁻³ is the reciprocal of three 2²s multiplied together.(2²)⁻³ = 2⁻⁶, because 2 × (-3) = -6
  3. Dividing powers with the same base subtracts the exponents. Subtracting a negative adds.2⁻³ ÷ 2⁻⁶ = 2³, because -3 - (-6) = 3
  4. Evaluate the single power.2³ = 8
Answer2³ = 8

Check it: Work it in fractions instead: 2⁵ × 2⁻⁸ = 32 × 1/256 = 1/8, and (2²)⁻³ = 4⁻³ = 1/64. Then 1/8 ÷ 1/64 = 64/8 = 8.

Common Mistakes with 8.EE.1

Multiplying the bases

3² × 3⁴ = 9⁶

Try this: Write out the factors once: two 3s times four 3s is six 3s, so the base stays 3 and the answer is 3⁶.

Reading a negative exponent as a negative number

5⁻² = -25

Try this: Continue the pattern 5² = 25, 5¹ = 5, 5⁰ = 1: each step divides by 5, so 5⁻² = 1/25.

Adding exponents in a power of a power

(4³)² = 4⁵

Try this: Write (4³)² as 4³ × 4³ and count: two groups of three 4s is six, so multiply exponents: 4⁶.

Where 8.EE.1 Fits

Comes Before6.EE.1Write and evaluate whole-number exponents, like 5³ = 125.5.NBT.2Use whole-number exponents to write powers of 10.
Alongside8.EE.2Undo squares and cubes with square and cube roots.8.EE.3Write very large and very small amounts with powers of 10.
Comes Next8.EE.4Multiply and divide in scientific notation, where these rules do the work.
HSN-RN.1Extend the rules to rational exponents, like 8 to the power one third.

Practice 8.EE.1

Math Worksheet GeneratorFree ToolA mixed page of expressions like 2⁵ × 2⁻⁸ that students rewrite as one power and then evaluate as a number or fraction.ExponentsGrade 8
Make a Worksheet

Quick Check

  1. Write 6⁷ ÷ 6⁹ as a fraction.
  2. Simplify (3⁻¹)² × 3⁵.
  3. Is 10⁰ equal to 0, 1 or 10?

8.EE.1: Other Names

8.EE.18.EE.A.1CCSS.MATH.CONTENT.8.EE.A.1

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.