Shortcut to Find the Fourth Power of any Two Digit Number

In this article we will explore a shortcut to find the fourth power of any 2 digit number. The approach will be similar to the shortcut to find the cube of any 2 digit number. I strongly suggest that you should check that first. 

Generic Form of 4th Power of 2 Digit Numbers

The generic form of fourth power of any two digit number can be algebraically expressed as:

(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4

We will split the above result in 2 lines. We start with 4th power of 1st digit and then keep multiplying with ratio of 2nd digit: 1st digit = b/a. The remaining will go in the next line. This can be written as –

= a4 +  a3b  +  a2b2   +  ab3   + b4   

             3a3b + 5a2b2 + 3ab3

__________________________________  Adding the above 2 lines, we get original result.

= a4 + 4a3b + 6a2b2 + 4ab3 + b4

Example of Shortcut to Find the 4th power of 2 Digit Numbers

To try this shortcut, let us consider a simple example i.e. 124

Here the first digit is 1 and its fourth power is also 1. The ratio of 2nd to the 1st digit is 2 (Ratio = b/a)

The remaining 4 terms can be obtained by multiplying each of the previous terms as shown :

124 =  1      2       4      8     16

6      20    24

_____________________
=  1    8      24     32    16

=  1    8      24     32    16

=  1    8      24     33      6

=  1    8      27      3      6

=  2    0       7      3      6

= 20736

Let us try another example. We will find out the 4th power of 91.

914 = 6561            729             81            9           1

2187           405            27

____________________________________

6561        2916             486         36           1

Keeping single digit in each step and carrying the remaining digits and adding to number on the left, we get the answer as 68574961

Tip to use the shortcut: If we memorize the fourth power of all the single digits (0-9), it will come very handy for using this trick of calculating fourth power of any two digit numbers. Find below the table of fourth power of first ten natural numbers –

Number

Fourth Power

1

1

2

16

3

81

4

256

5

625

6

1296

7

2401

8

4096

9

6561

10

10000

Do you think this shortcut can be applied for calculating fourth power of a number?

3 Comments
  1. kaustuv panda
  2. ahmed41
  3. Anusia

Leave a Reply

Your email address will not be published.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