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αAπΣ∞∂θ√x²≠∫÷≤%+−½αβΔλφ³≈∑°
  1. Home/
  2. Mathematics/
  3. Grade 8/
  4. Unit 1/
  5. Properties of Exponents
Grade 8 · Unit 1Topic 1 of 3~24 min

Properties of Exponents

Use the product, quotient, and power rules to simplify expressions.

All topics in this unit
αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 1 · Learn

Walkthrough

Read this first — it covers the idea in plain language with a worked example.

Exponents are repeated multiplication

2⁴ means 2 × 2 × 2 × 2 = 16. The base is 2 and the exponent is 4.

The key rules

  1. 1Product rule: same base, add exponents — x³ · x² = x⁵.
  2. 2Quotient rule: same base, subtract exponents — x⁵ ÷ x² = x³.
  3. 3Power rule: power of a power, multiply exponents — (x³)² = x⁶.
  4. 4Zero exponent: any nonzero base to the 0 power is 1.
Worked example

Simplify x⁴ · x³ ÷ x².

  1. →Multiply: x⁴ · x³ = x⁷ (add 4 + 3).
  2. →Divide: x⁷ ÷ x² = x⁵ (subtract 7 - 2).

Watch out

A negative exponent means a reciprocal: x⁻² = 1 / x². It does not make the number negative.

αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 2 · Watch

Video walkthrough

A short video that walks through this topic.

Math Antics

Exponents

What exponents mean and how to work with them.

Watch on YouTube
αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 3 · Practice

Practice

Try a worksheet or work through some problems before the quiz.

Khan Academy

Exponent properties

Open resource
Math Worksheets 4 Kids

Exponents worksheets

Open resource
πΣ√≠≤+αβΔπΣx²θ÷+
Step 4 · Check

Quick check

A couple of questions to make sure this topic stuck. Retake as many times as you want.

Properties of Exponents

Question 1 of 3

Easy

Simplify: x⁵ · x³.

αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
←Back toUnit 1 overview→Next up · Topic 2 of 3Scientific Notation