A Key To The Laws Of Exponents, Rules and Examples - GMS - Learning Simply
Students' favourite free learning app with LIVE online classes, instant doubt resolution, unlimited practice for classes 6-12, personalized study app for Maths, Science, Social Studies, video e-learning, online tutorial, and more. Join Telegram

A Key To The Laws Of Exponents, Rules and Examples

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,
Please wait 0 seconds...
Scroll Down and click on Go to Link for destination
Congrats! Link is Generated

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 ÷ 3= 3{(4-2)} = 32

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

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

(ap)= 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

Example 3:

What is the value of 2 power 9 and 2 power 7?

Solution:

2 power 9 can be represented as 29.

The value of 2 power 9 = 29 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 512

The value of 2 power 7 = 27 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128

Practice Problems

  1. Find the value of (43)2.
  2. What is the value of 6-2. 65?
  3. Evaluate: (0.5)2
  4. Find the value of the product of 2 power 7 and 2 power 9.

Thus, we have seen this basic introduction and examples of the laws of exponents.

About the Author

At the helm of GMS Learning is Principal Balkishan Agrawal, a dedicated and experienced educationist. Under his able guidance, our school has flourished academically and has achieved remarkable milestones in various fields. Principal Agrawal’s visio…
Cookie Consent
We serve cookies on this site to analyze traffic, remember your preferences, and optimize your experience.
Oops!
It seems there is something wrong with your internet connection. Please connect to the internet and start browsing again.
AdBlock Detected!
We have detected that you are using adblocking plugin in your browser.
The revenue we earn by the advertisements is used to manage this website, we request you to whitelist our website in your adblocking plugin.
Site is Blocked
Sorry! This site is not available in your country.