Exponents Educational Resources

Exponents represent an abstract unit whose value correlates to a given number. In a way, exponents are like shorthand for multiplication; they indicate the number of times a given value will be multiplied by itself, so they pack a lot of power. Use the resources on this page to develop a clearer understanding of why and how 2³=2 × 2 × 2.

An exponent is a useful tool that shortens mathematical formulas used in economics, chemistry, computer science, and many other fields. Mathematical operations involving exponents contain two numbers, a base (b) and an exponent (n). The exponent indicates how many times the base must be multiplied by itself. Thus, exponentiation results depend on the values of both base and exponent; are they positive or negative, integers or fractions?

Basic exponent uses include:

• “b squared” or “b to the power of 2” = b² = b × b
• “b cubed” or “b to the power of 3” = b³ = b × b × b

Interesting exponent results occur when the exponent is 0 or below:

• b⁰ = ^b1⁄_b = 1


• b^-1 = ^b0⁄_b = ¹⁄_b


• b^-n = ¹⁄_bⁿ

When the base is 0, no matter the exponential value, the resulting unit will always be 0:

• 0³ = 0 × 0 × 0 = 0
• 0¹⁵ = 0

It is important to understand the basics of using exponents. You will soon find them necessary to calculate area, perimeter, and volume, among other values:

• The area of a square: A = s²
• The area of a circle: A = πr²
• The volume of a cube: V = s³
• The volume of a sphere: V = ⁴⁄₃πr³
• The perimeter of a right triangle: P = a+b+√a²+b²
• And more!

Practice calculating mathematical operations containing exponents by utilizing the resources on this page, and your skills will increase exponentially!