# LAWS OF EXPONENTS

## What is exponents?

The exponents of a number says how many times to use the number in a multiplication.

5³ = 5 x 5 x 5

In words 5³ could be called as 5 to the power 3 or 5 cube.

Question 1 :

Express m x m x n x n in exponential form.

Solution :

Here m is repeating 2 times. To write m x m in the exponential form, we have to write it as m².

Like that n is also repeating 2 times. To write n x n in the exponential form, we have to write it as n²

Hence, the exponential form of m x m x n x n = m² x n²

Question 2 :

Express 5 x 5 x 5 in exponential form.

Solution :

Here 5 is repeating 3 times. To write 5 x 5 x 5 in the exponential form we have to write it as 5³

## Basic laws of exponents:

Rule 1 :

Whenever we want to simplify two or more terms which are having the same base, then we have put only one base and add the powers.

Rule 2 :

Whenever we want to simplify the terms which are dividing with the same base, we have to put only one base and subtract the powers.

Rule 3 :

Whenever we have power to the power, we have to multiply both powers.

Rule 4 :

Anything to the power zero is 1.

Rule 5 :

If we have same power for 2 or more terms which are multiplying or dividing then we have to distribute the power for those terms which are multiplying or dividing inside the bracket.

Note :

This rule is not applicable if two or more terms which are adding and subtracting.

For example (x + y) ^m = (x^m + y^m) is not correct

## How to move an exponents or powers to the other side ?

 that is x = 4² If the power goes from one side of equal sign to the other side, it will flip.

## What is exponent and power?

The other names of exponent are index and power.

Other things:

Point 1:

If we don't have any number in the power then we have to consider that there is 1

Point 2:

In case we have negative power for any fraction and if we want to make it as positive, we can write the power as positive and we should write its reciprocal only. For example

## Example problems using laws of exponents:

Question 3 :

Simplify 4 x ^(-1)/x^(-1/3)

Solution :

 Question 4 :Find the value of 2(256) ^(-1/8)Solution :  =  2 (2^8)^(-1/8)  =  2 (2^-1)  =  2/2  =  1

Question 5 :

Find the value of

Question 6 :

Find the value of x^(a - b) x^(b - c) x^(c - a)

Solution :

Question 7 :

Find the value of (8/27)^(-1/3) (32/243)^(-1/5)

Solution :

You can try these problems based on laws of exponents.

1. Express  7 x 7 x 5 x 5 in exponential form.

2. Express 13 x b x b x b x b in exponential form.

3. Express 17 x 17 x w x w x w in exponential form.

4. Express 5 x 5 x p x p x p in exponential form.

5. Express  n x n x n x b x b in exponential form.

6. Express  9 x 9 x 9 x c in exponential form.

7. Express 4 x 4 x 4 x k x k in exponential form.

8. Express 2 x 2 x 2 x r x r in exponential form.

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