Enter a base number and an exponent (the power). Press Calculate to see the result, along with each multiplication step written out. You can use negative bases and negative exponents. The result updates with a visual scale bar showing how large the answer is relative to the base.
An exponent is shorthand for repeated multiplication. The expression 2^5 means 2 multiplied by itself 5 times: 2 x 2 x 2 x 2 x 2 = 32. The bottom number is the base. The top number is the exponent, also called the power.
Exponents grow fast. 2^10 is already 1,024. That is why they appear everywhere from computer memory (powers of 2) to scientific notation (powers of 10 for very large or very small numbers).
| Rule Name | Formula | Example |
|---|---|---|
| Product rule | a^m x a^n = a^(m+n) | 2^3 x 2^4 = 2^7 = 128 |
| Quotient rule | a^m / a^n = a^(m-n) | 3^5 / 3^2 = 3^3 = 27 |
| Power rule | (a^m)^n = a^(m x n) | (2^3)^2 = 2^6 = 64 |
| Zero exponent | a^0 = 1 | 7^0 = 1 |
| Negative exponent | a^(-n) = 1 / a^n | 2^(-3) = 1/8 = 0.125 |
Roots are the inverse of powers. The square root asks: what number squared gives this result? The square root of 25 is 5 because 5^2 = 25. You can write square root as a fractional exponent: 25^(1/2) = 5.
The cube root asks: what number cubed gives this result? The cube root of 27 is 3 because 3^3 = 27. Written as a fractional exponent: 27^(1/3) = 3.
