# 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} = a^{4} + 4a^{3}b + 6a^{2}b^{2} + 4ab^{3} + b^{4}**

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

**= a ^{4} + a^{3}b + a^{2}b^{2} + ab^{3} + b^{4 }**

** 3a ^{3}b + 5a^{2}b^{2} + 3ab^{3}**

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

**= a ^{4} + 4a^{3}b + 6a^{2}b^{2} + 4ab^{3} + b^{4}**

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

To try this shortcut, let us consider a simple example i.e. **12 ^{4}**

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

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

12^{4} = 1 2 4 8 16

6 20 24

_____________________

= 1 8 24 32 16

= 1 8 24 32 _{1}6

= 1 8 24 _{3}3 6

= 1 8 _{2}7 3 6

= 2 0 _{ }7 3 6

= 20736

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

91^{4} = 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?**

plzz give some more examples……

Fourth power of any number .

I enjoyed this article.

Hey,this is quite helpful. I have got this maths phobia. I think it helped me a lot.