# Fraction exponent calculator

Written as bn, involving two numbers, the bottom b, and therefore the exponent or power n, and pronounced as "b raised to the facility of n".

#### Input

$$x=10,\ n=3,\ d=2$$

#### Solution

$$10^{\frac{3}{2}}$$ $$= \sqrt{10^{3}}$$ $$= \sqrt{1000}$$ The principal, real, root of: $$\sqrt[2 ]{1000}$$ $$= 31.6227766$$

#### Formula :

$$\large x^{\frac{n}{d}} \normalsize = \; ?$$

# About the fraction exponent calculator

Written as bn, involving two numbers, the bottom b, and therefore the exponent or power n, and pronounced as "b raised to the facility of n". When n may be a positive integer, exponentiation corresponds to repeated multiplication of the base: that’s, bn is that the product of multiplying n bases:

bn = b x ….. x b/ n times.

The exponent is typically shown as a superscript to the proper of the bottom. therein case, bn is named "braised to the nth power", "braised to the facility of n", "the nth power of b", "b to the nth power", or most briefly as "b to the nth".

One has b1 = b, and, for any positive integers m and n, one has bn ⋅ bm = bn+m. to increase this property to non-positive integer exponents, b0 is defined to be 1, and b−n (with n a positive integer and b not zero) is defined as 1/bn. especially, b−1 is adequate to 1/b, the reciprocal of b.

## Fractional exponents with the numerator adequate to 1

The fractional exponents are how of expressing powers also as roots in one notation.

What does it mean, exactly? Let's have a glance at a couple of simple examples first, where our numerator is adequate to 1:

64 (1/2) = √64

27 (1/3) = ³√27

From the equations above we will deduce that:

An exponent of 1/2 maybe a root

An exponent of 1/3 maybe a root

An exponent of 1/4 maybe the fourth root

An exponent of 1/k may be a kth root

Formula: exponent of 1/k adequate to k-th root

But why is it so? We'll attempt to prove it:

Let's use the law of exponents which says that we will add the exponents when multiplying two powers

Those have an equivalent base:

xa+b = xa * xb

So, for instance, if n = 2

X² = x¹âº¹ = x¹ * x¹ = x * x

Try this with any number you wish, it is often true!

Then, let's check out the fractional exponents of x:

x = x¹ = x (1/2 + 1/2) = x (1/2) * x (1/2)

How does one call variety which - when multiplied by itself - gives another number? It is a root, of course! So we acknowledged that:

X (1/2) = √x

If you wish, you'll analogically check other roots, e.g. the cube root:

x = x (1/3 + 1/3 + 1/3) = x (1/3) * x (1/3) * x (1/3) = ³√x * ³√x * ³√x

So x (1/3) = ³√x

Now we all know that x to the facility of 1 third is adequate to the root of x.

### How to use this calculator fraction exponent.

This calculator fraction exponent is a tool that will make your life easy while you solve problems related to the fraction exponent.

As we know in fraction exponent we have three value,

• The first one is x that is called a base value
• The second one is n that is called a nominator and
• The third one is the denominator d.

Now, based on this fraction exponent we have provided 3 boxes.

Now in their boxes, you have filled the proper value

After you will input the value in it you have to click on the calculate button which is given below to get the Calculation result.

You don’t need to worry about the formula because we have created this tool including the formula in it.

So this is how this tool work, you can also bookmark this tool that you can get help when you need it.

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