What Is an Exponent?
An exponent tells you how many times to multiply a number by itself.
In 3⁴, the 3 is the base and the 4 is the exponent. It means: 3 × 3 × 3 × 3 = 81.
Read it as "3 to the 4th power" or "3 to the 4th."
Special exponents
- Squared (²): 5² = 5 × 5 = 25. Called "squared" because a square with side 5 has area 25.
- Cubed (³): 5³ = 5 × 5 × 5 = 125. Called "cubed" because a cube with side 5 has volume 125.
- To the 1st power: 5¹ = 5. Any number to the 1st power is itself.
- To the 0th power: 5⁰ = 1. Any non-zero number to the 0th power is 1.
How exponents connect to other math
- Multiplication chain: Just as multiplication is repeated addition (3 × 4 = 3 + 3 + 3 + 3), exponents are repeated multiplication (3⁴ = 3 × 3 × 3 × 3).
- Powers of 10: 10¹ = 10, 10² = 100, 10³ = 1,000. The exponent equals the number of zeros. This connects to place value.
- Scientific notation: Large numbers like 4.5 × 10⁶ use exponents to express magnitude. See scientific notation.
- Square roots: √25 = 5 because 5² = 25. Square roots undo squaring.
Common confusion
The most common error: confusing 3⁴ with 3 × 4. They are very different:
- 3⁴ = 3 × 3 × 3 × 3 = 81
- 3 × 4 = 12
Always expand the exponent to check: "3 to the 4th means 3, times 3, times 3, times 3."
For a full teaching guide on exponents, see How to Teach Exponents.