Exponents and Scientific Notation

Lesson 8 of 10Grades 8–9

Exponents represent repeated multiplication. 2⁵ = 2×2×2×2×2 = 32. The exponent rules let you simplify expressions without multiplying everything out. Scientific notation uses powers of 10 to write very large or small numbers compactly.

Key Concepts

Exponent Rules

Product rule: xᵃ × xᵇ = xᵃ⁺ᵇ. Quotient rule: xᵃ ÷ xᵇ = xᵃ⁻ᵇ. Power rule: (xᵃ)ᵇ = xᵃᵇ. Zero exponent: x⁰ = 1 (for x ≠ 0). Negative exponent: x⁻ⁿ = 1/xⁿ. These rules work for any base.

Scientific Notation

6.02 × 10²³ (Avogadro's number) and 1.6 × 10⁻¹⁹ (electron charge in coulombs) are in scientific notation. The coefficient must be ≥1 and <10. Move the decimal point: 3,400,000 = 3.4 × 10⁶ (moved 6 places left). 0.000047 = 4.7 × 10⁻⁵ (moved 5 places right).

Operations with Scientific Notation

Multiply: multiply coefficients, add exponents. (3×10⁴)(2×10³) = 6×10⁷. Divide: divide coefficients, subtract exponents. Add/Subtract: convert to the same power of 10 first, then add/subtract coefficients.

🆕 Exponent and Scientific Notation Explorer

Enter a number to convert to scientific notation, or check an exponent rule.

Quick Rules Reference

      x³ × x⁴ = x⁷  (add exponents)

      x⁵ ÷ x² = x³  (subtract exponents)

      (x²)³ = x⁶    (multiply exponents)

      x⁰ = 1         (anything to zero = 1)

      x⁻² = 1/x²    (negative = reciprocal)

✅ Check Your Understanding

1. What is x³ × x⁴?

2. What is x⁰ equal to (x ≠ 0)?

3. 3,400,000 in scientific notation is...