Exponents represent repeated multiplication, just as multiplication represents repeated addition. The expression 3⁴ means 3 × 3 × 3 × 3 = 81. This compact notation is essential for expressing very large and very small numbers efficiently.

Students begin with squares (n²) and cubes (n³), which connect to geometry — the area of a square and the volume of a cube. Recognizing perfect squares (1, 4, 9, 16, 25...) and perfect cubes (1, 8, 27, 64...) builds number fluency.

Exponent laws simplify calculations with powers. When multiplying powers with the same base, add the exponents: 2³ × 2⁴ = 2⁷. When dividing, subtract: 2⁵ ÷ 2² = 2³. Any number raised to the zero power equals 1. These rules make complex calculations manageable.

Scientific notation uses exponents to express very large or small numbers. The speed of light is about 3 × 10⁸ meters per second. A water molecule is about 2.75 × 10⁻¹⁰ meters wide. This notation is essential in science, engineering, and computing.