Example 1
- x = 8
- m = 1
- n = 3
2
What is 8^(1/3)? 2. The cube root of 8.
Fractional power
Type x, numerator m and denominator n. A fractional power is x^(m/n). 8, 1 and 3 give 2. 16, 1 and 2 give 4. 27, 2 and 3 give 9.000000.
n = 0 returns 0, not Infinity. 27^(2/3) in machine float is 8.999999999999998, so the result is 9.000000, not a bare 9.
Results
Enter data and click Calculate.
How it works
A fractional power is x to the power m/n. The calculator raises a to the power b/c. 8, 1 and 3 is the cube root of 8 and gives 2. 16, 1 and 2 is the square root and gives 4.
The fields are x, m and n. m is the numerator, n the denominator. 27, 2 and 3 means 27^(2/3), the square of the cube root. In a notebook, 9. Here 27 to the power 2/3 is 8.999999999999998, so the result is 9.000000, not an integer 9.
When n = 0 the implementation does not divide. It returns 0. That is not 27^∞, only the branch at a zero denominator. x = 0 and a positive m/n give 0.
The nth root is on the neighbouring page and computes x^(1/n), with no separate numerator m. An ordinary power takes one exponent, not a fraction from two fields.
The header units switch does not multiply anything. 8, 1 and 3 stay 2 whatever the label says.
8, 1 and 3 give 2. 16, 1 and 2 give 4. 27, 2 and 3 give 9.000000. When n = 0 the result is 0.
Formula
x^(m/n) = Math.pow(x, m/n), when n ≠ 0; otherwise 0
How to use
- Type x, m and n, for example 8, 1 and 3.
- Click Calculate. The fractional power comes out 2.
- 16, 1 and 2 give 4. 27, 2 and 3 give 9.000000.
- When n = 0, the result is 0, not Infinity.
- An nth root lives on the neighbouring card.
8, 1 and 3 give 2
A fractional power is x^(m/n). 8, 1 and 3 give 2. 16, 1 and 2 give 4. 27, 2 and 3 give 9.000000.
- power
- x to the m/n. 8^(1/3) = 2. 16^(1/2) = 4.
- fractional
- The exponent is the fraction m/n, not one number. 27, 2 and 3 give 9.000000.
- denominator
- Field n. Zero in the denominator returns 0, not Infinity.
Examples
Example 2
- x = 16
- m = 1
- n = 2
4
What is 16^(1/2)? 4. The square root of 16.
Example 3
- x = 27
- m = 2
- n = 3
9.000000
What is 27^(2/3)? 9.000000. machine float misses 9, the calculator keeps six decimals.
Related calculators
Common questions
What is 8^(1/3)?
2. The cube root of 8. m = 1, n = 3.
What does fractional power mean?
x to the power m/n. Numerator m, denominator n. The calculator raises x to the power m/n.
What is 16^(1/2)?
4. The square root of 16.
What is 27^(2/3)?
9.000000. In a notebook, 9. Here 8.999999999999998 and six decimal places.
What if n = 0?
The calculator returns 0. It does not divide by zero and does not print Infinity.
Which field is the denominator?
The third, n. The second is numerator m. The first is x.
How is this different from the nth root?
There you always have 1/n. Here numerator m can be 2, as in 27^(2/3).
Does a negative x pass?
It depends on the fraction. A negative base and a fraction can be a blank value. This calculator does not promise complex numbers.
Where is an ordinary power?
On the power page. 2 to the 10th is 1024. Here you always have two exponent fields.
Does a comma in 8.0 work?
Yes. 8.0 and 8,0 with 1 and 3 both give 2.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.