### Exponents & Roots

**1. Exponents **

Exponents are used to represent the repeated multiplication of a number by itself. Some rules of exponents are given below: –

For example, 2^{3} = 2 × 2 × 2 = 8

In the expression, 2^{3}, 2 is called the base, 3 is called the exponent, and we read the expression as “2 to the third power.”

When the exponent is 2, we call the process squaring.

For example,

5^{2} = 25, is read as “5 squared is 25”.

6^{2} = 36, is read as “6 squared is 36”.

When negative numbers are raised to powers, the result may be positive or negative. A negative number raised to an even power is always positive, and a negative number raised to an odd power is always negative.

For example,

(−3)^{4} = −3 × −3 × −3 × −3 = 81

(−3)^{3}= −3 × −3 × −3 = −27

Take note of the parenthesis: (−3)^{2} = 9, but −3^{2} = −9

**2. Square Roots**

A square root of a non-negative number *n* is a number *r* such that *r*^{2} = *n*.

For example, 5 is a square root of 25 because 5^{2} = 25.

Another square root of 25 is −5 because (−5)^{2} is also equals to 25.

### Rules for Square Roots

Here are some important rules regarding operations with square roots, where *x* > 0 and *y* > 0

For example,

8 has one cube root.

The cube root of 8 is 2 because 2^{3} = 8.

−8 has one cube root. The cube root of −8 is −2 because (−2)^{3}= −8

8 has two fourth roots.

because 2^{4} = 16 and (−2)^{4} = 16