This fraction exponent calculator is designed to compute mathematical expressions involving fractional exponents using x^(a/b) = (x^a)^(1/b) = ∛(x^a) formula.
The expression 2^(3/4) represents 2 raised to the power of 3/4, which is a fractional exponent. A fraction exponent calculator can quickly and accurately evaluate this expression, saving time and reducing errors in manual calculations.
Fraction Exponent Calculator
| Base (x) | Exponent (a/b) | Calculation | Result (rounded to 4 decimal places) |
|---|---|---|---|
| 2 | 1/2 | 2^(1/2) | 1.4142 |
| 5 | 3/4 | 5^(3/4) | 3.3437 |
| 10 | 2/3 | 10^(2/3) | 4.6416 |
| 7 | 5/2 | 7^(5/2) | 129.6440 |
| 4 | 3/5 | 4^(3/5) | 2.2974 |
| 6 | 1/3 | 6^(1/3) | 1.8171 |
| 9 | 4/3 | 9^(4/3) | 20.7846 |
| 3 | 7/6 | 3^(7/6) | 3.5569 |
| 16 | 3/2 | 16^(3/2) | 64.0000 |
| 8 | 2/3 | 8^(2/3) | 4.0000 |
| 27 | 4/3 | 27^(4/3) | 81.0000 |
| 64 | 1/2 | 64^(1/2) | 8.0000 |
| 81 | 1/4 | 81^(1/4) | 3.0000 |
| 100 | 1/2 | 100^(1/2) | 10.0000 |
| 125 | 3/2 | 125^(3/2) | 1250.0000 |
| 343 | -1/3 | 343^(-1/3) | 0.4642 |
| 49 | 2/2 | 49^(2/2) | 49.0000 |
| 16 | 5/4 | 16^(5/4) | 32.0000 |
| 2 | -1/2 | 2^(-1/2) | 0.7071 |
| 3 | 3/2 | 3^(3/2) | 5.1962 |
Fractional Exponent Formula
x^(a/b) = (x^a)^(1/b) = ∛(x^a)Where:
- x is the base number
- a is the numerator of the fractional exponent
- b is the denominator of the fractional exponent
Let’s break this down with some examples:
2^(1/2) = √2 ≈ 1.414: This represents the square root of 2.
8^(2/3) = ∛(8^2) = ∛64 = 4: This calculation involves taking the cube root of 8 squared.
5^(3/4) = (5^3)^(1/4) ≈ 3.344: We first calculate 5^3 = 125, then take the fourth root of the result.
How to do a fraction exponent?
- Recognize the base (x) and the fractional exponent (a/b).
- Use the fractional exponent formula x^(a/b) = (x^a)^(1/b).
- Calculate the first part: Compute x^a.
- Find the root: Calculate the b-th root of the result from step 3.
Let’s work through an example: 3^(2/5)
Base (x) = 3, Exponent (a/b) = 2/5
Apply the formula: 3^(2/5) = (3^2)^(1/5)
Calculate 3^2 = 9
Find the 5th root of 9: ∜9 ≈ 1.552
Therefore, 3^(2/5) ≈ 1.552
What is 3 to the power of 2 as a fraction?
The expression 3 to the power of 2 is typically written as 3^2.
3^2 = 3^(2/1) = 9
In this case:
- The base (x) is 3
- The numerator (a) is 2
- The denominator (b) is 1
Using the fractional exponent formula:
3^(2/1) = (3^2)^(1/1) = 9^1 = 9
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