Base · exponent · repeated multiplication
POWERS &
EXPONENTS
A power records repeated multiplication compactly. For a positive whole-number exponent, the exponent tells how many factors of the same base are multiplied together.
Anatomy of a Power
4
Base
3
Exponent
Base: the repeated factor.
Exponent: for a positive whole-number exponent, the number of times the base appears as a factor.
Evaluate: multiply those factors together.
4³ = 4 × 4 × 4 = 64
Squared (x²)
The name connects to the area of a square with side length x.
Cubed (x³)
The name connects to the volume of a cube with side length x.
Growth Model
The Power Visualizer
Base Number2
The Modifier (n)3
Multiplication
2 × 3
2 + 2 + 2
= 6
Exponentiation
2 3
2 × 2 × 2
= 8
Scale Comparison
6
Linear
8
Exponent
Scientific Notation
Powers of ten provide a compact way to represent very large or very small values. Scientific notation writes a number as a coefficient times a power of ten.
Standard FormScientific Notation
3,200,0003.2 × 106
Reference & Check
Knowledge Check: Powers1 / 3
What does 3⁴ mean mathematically?
Connect Forward
Powers become structural parts of algebraic terms, so recognizing bases and exponents prepares you to read expressions accurately.