# How To Solve Negative Exponents

Before solving negative exponents , let’s have an overview of exponents followed by negative exponents examples

**Description:**

Exponents are one of the important algebraic operators that determines how many times a number is to be multiplied by itself. A number raised to an exponent can be shown as

where ‘X’ is the coefficient

‘a’ is the base

‘n’ is the exponent

The positive or negative signs of ‘n’ exponent indicate whether it is a positive exponent or negative exponent respectively. In the above expression , a is raised to a negative exponent. If it is written as

In this expression , a is raised to a negative exponent. Furthermore, we can write this expression as

For coefficient X=1 , the above equation becomes

This implies that sign of an exponent can be changed by changing its position (either numerator or denominator) in the fraction line. Secondly , a number raised to a negative exponent ‘a^{-n} ‘ is equivalent to its reciprocal ‘ 1/a^{n ‘}.

For n =2 , a = 2 , we have the above equation as

**Negative Exponents Examples**

The below given examples of negative exponents will further tell you how to solve negative exponents

**Solution
**

By taking reciprocals of numbers raised to negative powers , we have positive exponents as

Expanding the numbers raised to positive exponents , we got

As the numbers raised to zero exponents are equivalent to 1. So , we have the above equation as

So , answer is 0.5

**Solution **

The square roots of numbers are equivalent to numbers raised to 1/2. So , we have

By rearranging powers , we have

Expanding the powers , we got

To solve the fractional exponent in (4)^{1/2} , we will first convert the base 4 to its exponential form

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