LAWS OF EXPONENTS

In the page " laws of exponents" we are going to learn about what does mean by exponents,what are laws used in exponents and example problems.

What is exponent?

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

for example 5³ = 5 x 5 x 5

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

Basic laws of exponents:

Rule 1:

When we have to simplify two or more the terms which are multiplying with same base,then we have to put the same base and add the powers.

Rule 2:

Whenever we have two terms which are diving with the same base,we have to put only one base and we have to 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,we have to apply the powers for every terms.

Note:

This rule is not applicable when two are 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 ?

If the power goes from one side of equal sign to the other side,it will flip.

that is x = 4²

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:

Incase 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:

Example 1:

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

Example 2:

Find the value of 2(256) ^(-1/8)

= 2 (2^8)^(-1/8)

= 2 (2^-1)

= 2/2

= 1

Example 3:

Find the value of

Example 4:

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

Let us see the next example of the topic " laws of exponents".

Example 5:

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

Now you can some practice question.You can try these problems based on laws of exponents.

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

2.Express 5 x 5 x 5 in exponential form.

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

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

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

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

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

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

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

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