Exponents and Roots: A Crash Course for Adults

Some calculations matter for a single decision; this one matters for years. Exponents and roots show up in compound interest, population growth, scientific notation and almost every formula worth knowing.

What an exponent is

Shorthand for repeated multiplication. 5³ = 5 × 5 × 5 = 125.

What a root is

The opposite. √125 (cube root) = 5.

Fractional exponents

x^(1/2) is √x. x^(1/3) is cube root. x^(2/3) = (x^2)^(1/3) = (cube root of x)².

Negative exponents

x^(-2) = 1/x². Used in scientific notation for tiny numbers.

Pro tips

• Anything to the 0 power equals 1 (by convention).
• Multiplying same-base exponents: add the exponents. x² × x³ = x⁵.

Frequently asked questions

What is e^x used for? Exponential growth/decay — compound interest, population, radioactive decay.

Why is 0⁰ disputed? Mathematically undefined in pure math; programming languages typically return 1.

The math is the easy part. Acting on what it tells you is where the real win lives.