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)represents2 raised to the power of 3/4, which is afractional exponent. A fraction exponent calculator can quickly and accurately evaluate this expression,saving timeandreducing errorsin 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:

xis thebase numberais thenumeratorof the fractional exponentbis thedenominatorof the fractional exponent

Let’s break this down with some **examples**:

2^(1/2)= √2 ≈ 1.414: This represents thesquare rootof 2.

8^(2/3)= ∛(8^2) = ∛64 = 4: This calculation involves taking thecube rootof 8 squared.

5^(3/4)= (5^3)^(1/4) ≈ 3.344: We first calculate 5^3 = 125, then take thefourth rootof 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 rootof 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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