Case 1
- Base
- 2
- Exponent
- 10
1,024.000000
Open with these valuesExponent Calculator
1,024.000000
Result: 1,024.000000The exponent says how many times the base multiplies itself, so 2^10 is 1024. A negative exponent is the reciprocal: 2^-3 is 1 ÷ 8 = 0.125. A fractional exponent is a root, so 9^0.5 is the square root of 9, which is 3.
Worked examples
Case 2
- Base
- 9
- Exponent
- 0.5
3.000000
Open with these valuesCase 3
- Base
- 2
- Exponent
- -3
0.125000
Open with these valuesHow it's calculated
result = base^exponent
- StepEnter the base — the number being multiplied.
- StepEnter the exponent — the power it is raised to.
- StepA negative exponent gives the reciprocal.
- ResultA fractional exponent gives a root.
Reference table
| Base, exponent | Read as | Result |
|---|---|---|
| 2, 10 | ten 2s multiplied together | 1024 |
| 3, 4 | 3 × 3 × 3 × 3 | 81 |
| 5, 2 | 5 squared | 25 |
| 10, 3 | 10 cubed | 1000 |
| 2, -3 | one over 2 cubed | 0.125 |
| 9, 0.5 | the square root of 9 | 3 |
| 7, 0 | any base to the power zero | 1 |
Questions
What is an exponent?
It tells you how many times to multiply a base by itself. In base^exponent the base is the number and the exponent is the power, so 2^10 means ten 2s multiplied together, which is 1024.
What does a negative exponent mean?
It means the reciprocal of the positive power, so 2^-3 is 1 ÷ 2^3 = 1 ÷ 8 = 0.125. The larger the negative exponent, the smaller the result, but it never turns negative by itself.
What does a fractional exponent mean?
A fractional exponent is a root. The power 0.5 is the square root, so 9^0.5 is 3, and 8^(1/3) is the cube root of 8, which is 2. Any fraction p/q means the q-th root of the base raised to the power p.
Why is anything to the power 0 equal to 1?
Dividing 2^1 by 2^1 gives 2^0, and any number divided by itself is 1, so the pattern only stays consistent if the power zero gives 1. That holds for 7 and for 1000 alike.
Why does the base have to be positive here?
Two inputs have no usable answer: a negative base with a fractional exponent, such as (-2)^0.5, has no real value at all, and zero raised to a negative power divides by zero. Keeping the base above zero rules both out instead of showing a misleading number.
Sources and last check
Information, not professional advice.