Negative exponents are a type of exponential notation and represent the reciprocal of an expression with a positive exponent.

**For example,** the expression “a^{-n}” represents the reciprocal of “a^{n}“.

In other words, if “a^{n}” = x, then “a^{-n}” = 1/x.

**For example**, if a^{2} = 9, then a^{-2} = 1/9.

**Some other examples of Negative Exponents:**

- 6
^{-1}is equal to 1/6 - Y
^{-4}is written as 1/y^{4} - (3x+2y)
^{-2}is equal to 1/(3x+2y)^{2}.

Negative exponents are used to simplifying expressions and to represent the **inverse of exponential functions**. They can also be used to represent very small numbers in scientific notation.

It is important to comprehend the laws for simplifying expressions with negative exponents, such as:

**1. Law of quotient **

When dividing two exponential expressions with the same base, the result is the difference between the exponents.

**For example**, a^{m} / a^{n} = a^{m – n}.

**2. Fractions with Negative Exponents
**

If a^{m} is an exponential expression, then we can express:

(a^{-m })^{(1/n) = } (1/a^m)^(1/n).

**For example**, (a^-2)^(1/3) = (1/a^2)^(1/3).

By using these rules, you can simplify expressions with negative exponents and manipulate them to solve mathematical problems.

### How to Solve Negative Exponents?

Here are some examples of solving the negative exponents.

**Example 1: Simplify 6x ^{-2}.**

**Solution:**

As Given expression 6x^{-2}

Using the rule, a^{-n} = 1/a^{n}

6x^{-2} = 6 (1/x^{2})

6x^{-2} = 6/x^{2}.