Exponents
Understanding exponents and exponential notation
Interactive Exponents Visualization
Introduction
An exponent (or power) tells us how many times to multiply a number (the base) by itself. Exponents provide a compact way to write repeated multiplication and are fundamental in mathematics.
Key Concepts:
- Base: The number being multiplied (e.g., in 2³, 2 is the base)
- Exponent: The number of times the base is multiplied (e.g., in 2³, 3 is the exponent)
- Power: The result of raising a base to an exponent (e.g., 2³ = 8)
- Exponential Growth: Values increase rapidly as the exponent increases
- Special Cases: Any number to the power of 0 equals 1, negative exponents create fractions
How to Use
- Visual Representation: See how exponents represent repeated multiplication
- Exponential Growth: Watch how values grow rapidly as the exponent increases
- Exponent Properties: Explore the rules for working with exponents
- Exponent Operations: Practice multiplying, dividing, and raising powers to powers
- Adjust the base and exponent to see how they affect the result
- Notice how exponential growth becomes very rapid for larger exponents
Exponent Information
Expression: 2^3
Expansion: 2 × 2 × 2
Result: 8
Visual Representation
Exponent Rules
Multiplying Powers:
a^m × a^n = a^(m+n)
Dividing Powers:
a^m ÷ a^n = a^(m-n)
Power of a Power:
(a^m)^n = a^(m×n)
Zero Exponent:
a^0 = 1 (for any a ≠ 0)
Negative Exponent:
a^-n = 1 / a^n
Fractional Exponent:
a^(1/n) = ⁿ√a (nth root)
Lessons
Individual learning units
Lessons coming soon