A Key To The Laws Of Exponents

Can you read 10,000,000,000,000,000,000,000? This massive natural number is not easy to read, recognize and evaluate. Exponents make it easy to read, recognize and evaluate very large numbers. Exponents are also called powers or indices. What is meant by exponents? What are the laws of exponents? How to apply the laws of exponents to simplify expressions? Let us take an overview of the laws of exponents.

A Key To The Laws Of Exponents

Rules of Exponents With Examples

Exponents are defined as a number that tells how many times we have to multiply the base number. It is written above the right side of the base number.

1. 52 = “5 raised to the power of 2” or “5 squared.”

2. 53 = “5 raised to the power of 3” or “10 cubed.”

Example 1 :10,000 = 10 x 10 x 10 x 10 = 104

The laws of exponents state the following rules to simplify the expressions. Some of them are as follows:

Rule 1: When the numbers having the same base are multiplied, add the exponents.

ap × aq = a(p+q)

a = base : p,q = exponents

Example 1: Let us calculate,

32×34

Solution:

32 × 34 =3{(2+4)} = 36

In the above example, the base numbers are the same. (i.e.,) 32 and 34. The sum of the powers is 6.

Rule 2: When the numbers having the same base are divided, subtract the exponents.

ap ÷ aq = a{(p-q)} i.e. a = base: p,q = exponents

Example 2: 34 ÷ 32 =?

Solution:

34 ÷ 32 = 3{(4-2)} = 32

In the above example, the bases are same. (i.e., 34 and 32).

Rule 3: Multiply the powers when the numbers are raised by another number.

(ap)q = a{(pxq)} =a{(pq)}

Example 3 : (23)2 =?

Solution: (23)2 = 2{(3×2)} = 26

Example problems

Example 1:

Multiplying powers with the same base

32 × 33 =?

Solution:

In the above example, as per rule 1, add the powers when the numbers are multiplied.

So,

32 × 33 = 3{(2+3)} = 35

Example 2:

Dividing powers with the same base

45 ÷ 42

Solution:

In the above example, as per rule 2, subtract the powers when the numbers are divided.

So,

45 ÷ 42 = 4{(5-2)} = 43

Thus, we have seen this basic introduction and examples of the laws of exponents. For the complete understanding of the topic, please visit our site or download the BYJU’S – The Learning App.

2 Comments

  1. #thanks a lot . #very helpful

  2. For 9th class maths I can’t understand please help me??

Leave a Comment

Your email address will not be published. Required fields are marked *

BOOK

Free Class