## Simplification of numbers with Fractional Exponents

The exponent (or Power, or Index) of a number says how many times to use a number in a multiplication.

For Example-

**2² = 2 × 2,****Or,**

**5³ = 5 × 5 × 5**

### Fractional Exponents-

But what if the exponent is in Fraction?

A

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A

**fractional exponent**is an alternate notation for expressing powers and roots together. For example, the following are equivalent. We write the power in the numerator and the index of the root in the denominator.*

**The fractional exponent of a number is actually its Root. like Square root, Cube root, 4th root, 5th root, etc. see-****Prove-**

Let's see an example proving that-

**Recall-**remember

**What the laws of exponent tell us how to handle exponent when we multiply-**

see this example- x² x² = (xx) (xx) = xxxx = x4

it shows that-

Now, Try this on a fractional exponent-

**Example:-**what is 1/2 power of 5 × 1/2 power of 5?

and, The number which gives another number when multiplied by itself, Called? The Square Root!

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