# Math՚s: Exponential Notation: Laws of Exponents when Powers Are Negative (For CBSE, ICSE, IAS, NET, NRA 2022)

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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:

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