Exponent Calculator
Solve bˣ = y for any one of the base, exponent or result, exactly where possible (8⁻⁴ = 1/4096, 27^(2/3) = 9).
Change the values and press Calculate to work out your own figures.
Fill in two of base, exponent and result; leave the third blank.
Show the working
- 8^4 = 4,096
How to use it
Fill in two of base, exponent and result; leave the third blank.
Number boxes accept whole numbers, decimals, fractions (3/4), powers (2^10), roots (sqrt(2)) and the constants pi and e. Show the working lists the steps.
Key facts
y = bˣ; x = ln y ÷ ln b; b = y^(1/x)
Negative and fractional exponents
b⁻ⁿ = 1 ÷ bⁿ, and b^(p/q) is the q-th root of b to the p.
Powers table
2¹⁰ = 1,024, 3¹⁰ = 59,049, 5¹⁰ = 9,765,625.
Powers
| n | 2ⁿ | 3ⁿ | 4ⁿ | 5ⁿ |
|---|---|---|---|---|
| 0 | 1 | 1 | 1 | 1 |
| 1 | 2 | 3 | 4 | 5 |
| 2 | 4 | 9 | 16 | 25 |
| 3 | 8 | 27 | 64 | 125 |
| 4 | 16 | 81 | 256 | 625 |
| 5 | 32 | 243 | 1,024 | 3,125 |
| 6 | 64 | 729 | 4,096 | 15,625 |
| 7 | 128 | 2,187 | 16,384 | 78,125 |
| 8 | 256 | 6,561 | 65,536 | 390,625 |
| 9 | 512 | 19,683 | 262,144 | 1,953,125 |
| 10 | 1,024 | 59,049 | 1,048,576 | 9,765,625 |
Questions
What is 8 to the power −4?
1/4096 = 0.000244140625.
What is 0⁰?
1, by convention.
Formulas
y = bˣ; x = ln y ÷ ln b; b = y^(1/x)
Sources
Limitations
- Expressions up to 500 characters; matrices up to 10 × 10.
- Big-number results up to 100,000 digits; factorials up to 10,000!.
- Numbers in words up to 10^102 (short scale).