How Exponents Work
An exponent (also called a power or index) tells you how many times to multiply a Base number by itself. It is usually written as a small number to the top right of the base. For example, in the expression 2³, 2 is the base and 3 is the exponent.
Instead of writing 2 × 2 × 2, we simply write 2³. The answer is 8.
Rules for Special Exponents
The Zero Power Rule
Any non-zero number raised to the power of 0 is always equal to 1.
Example: 5⁰ = 1, and 1,000,000⁰ = 1.
Negative Exponents
A negative exponent tells you to divide 1 by the base raised to that power. It essentially creates a fraction.
Example: 2⁻³ = 1 / (2³) = 1 / 8 = 0.125.
Roots and Fractional Exponents
Roots are the exact opposite (the inverse) of exponents. If 3² = 9, then the square root of 9 is 3.
In advanced mathematics, roots are actually just fractional exponents. Writing the square root of 16 is mathematically identical to writing 16 to the power of 1/2. Writing the cube root of 27 is identical to writing 27^(1/3).