Exponent Calculator
Visual Grid
How to Use This Calculator
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.
What Exponents Mean
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).
The Exponent Rules
| 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 |
Square Roots and Cube Roots
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.
Common Mistakes to Avoid
- Thinking 2^3 means 2 x 3 = 6. It actually means 2 x 2 x 2 = 8. The exponent counts multiplications, not the size of the multiplier.
- Forgetting that any number to the power 0 equals 1. This surprises students who expect the answer to be 0.
- Confusing a negative base with a negative exponent. (-2)^3 = -8 but 2^(-3) = 1/8. These are very different things.
- Applying product rule when the bases are different. You can only add exponents when multiplying terms with the same base.