LESSON 9
EXPONENTS
The Power of Repeated Multiplication
What is an Exponent?
An exponent tells us how many times to multiply a number by itself. In the expression 2³, the number 2 is called the base and the number 3 is the exponent (or power). It means 2 × 2 × 2 = 8.
Exponents are a shorthand for repeated multiplication, just as multiplication is a shorthand for repeated addition. They appear throughout science, engineering, and everyday life — from measuring area and volume to describing very large or very small numbers.
Squares and Cubes
When a number is raised to the power of 2, we say it is squared. When raised to the power of 3, we say it is cubed. These are the most common exponents and connect directly to geometry — squaring gives area, cubing gives volume.
Laws of Exponents
There are key rules for working with exponents. When multiplying same bases, add the exponents. When dividing same bases, subtract the exponents. When raising a power to a power, multiply the exponents. Any number raised to the power of zero equals 1.
Negative Exponents
A negative exponent means we take the reciprocal of the base raised to the positive version of that exponent. So 2⁻³ means 1 divided by 2³. Negative exponents are used to express very small numbers and are common in scientific notation.
Scientific Notation
Scientific notation uses powers of 10 to write very large or very small numbers compactly. A number in scientific notation is written as a value between 1 and 10 multiplied by a power of 10. It is essential in science and engineering.
Key Facts
Any number raised to the power of 1 equals itself. Any number raised to the power of 0 equals 1 (except 0⁰, which is undefined).
The number of atoms in the observable universe is estimated at about 10⁸⁰ — a 1 followed by 80 zeros. Exponents make such numbers writable.
Perfect squares (1, 4, 9, 16, 25...) are numbers that result from squaring whole numbers. Recognizing them speeds up many calculations.
Computer storage uses powers of 2: 1 kilobyte = 2¹⁰ = 1,024 bytes. Exponents are fundamental to how computers work.