**What is exponents ? **

The exponent of a number tells that how many times we use that number in a multiplication.

For example,

5³ = 5 ⋅ 5 ⋅ 5

Here 5 is base and 3 is called as power or exponent.

#### How to write the given product in exponential form ?

a ⋅ a ⋅ a ⋅ a = a⁴ (The variable a is multiplied 4 times itself. So, we write a and write 4 in the power)

a ⋅ a ⋅ c ⋅ c ⋅ c = a² ⋅ c³ (The variable a is multiplied 2 times and c is multiplied two times).

**What is radical ?**

In mathematics, a radical expression is defined as any expression containing a radical (√) symbol.

The exponential form of a ^{n}√a is a^{1/n}

For example, ∛5 can be written in index form as

∛5 = 5 ^{1/3}

## Basic Rules in Exponents and Radicals

### Rules in Exponents :

#### x^{m }⋅ x^{n } = x^{(m + n)}

#### x^{m}/x^{n } = x^{(m – n)}

#### (x^{m})^{n } = x^{mn}

#### x^{0} = 1

### Rules in Radicals :

#### (^{n}√a)^{n } = a

^{n}√a x ^{n}√b = ^{n}√(a x b)

** **^{n}√a / ^{n}√b = ^{n}√(a / b)

**(**^{n}√a)^{m } = a^{m/n}