# Math's: Exponential Notation: Laws of Exponents when Powers Are Negative

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## Laws of Exponents

Laws of Exponents are the rules that tell us how to do the mathematical operations (addition, subtraction, multiplication and division) of numbers in exponential form.

**Laws of exponent are:**

(i) When we multiply two numbers having same base, then we add the powers as given below

Example-

(ii) When we divide two numbers having the same base, we subtract the powers as below-

Example-

(iii) When the products of two numbers raise a power, then raise the same power to both of them and multiply them as below-

Example-

(iv) When the division of two numbers raise a power, then raise the same power to both of them and divide them as below-

Example-

(v) If a number raise a power to a power, multiply the powers as below-

Example-

(vi) Any non-zero rational number raised to the power zero equals to 1

Example-

## Laws of Exponents when Powers Are Negative

When any number has a negative power, that equals to the reciprocal of the same number having the same but positive power.

Example-

The other laws of applies in the same way is in case of positive powers.

## Laws of Exponents when Powers Are in Fraction

When any number has a power in fraction say in form, then that equals to the qth root of that number raised to the power p.

Example-

The other laws of applies in the same way is in case of integral powers.

1. Find the value of

Solution:

2. Simplify the following and express the result in exponential form.

Solution: