# Smallest N digit number which is a perfect fourth power

Given an integer **N**, the task is to find the smallest **N-digit** number which is a perfect fourth power.

**Examples:**

Input:N = 2

Output:16

Only valid numbers are 2^{4}= 16

and 3^{4}= 81 but 16 is the minimum.

Input:N = 3

Output:256

4^{4}= 256

**Approach:** It can be observed that for the values of **N = 1, 2, 3, …**, the series will go on like **1, 16, 256, 1296, 10000, 104976, 1048576, …** whose **N ^{th}** term will be

**pow(ceil( (pow(pow(10, (n – 1)), 1 / 4) ) ), 4)**.

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach ` `#include <bits/stdc++.h> ` ` ` `using` `namespace` `std; ` ` ` `// Function to return the smallest n-digit ` `// number which is a perfect fourth power ` `int` `cal(` `int` `n) ` `{ ` ` ` `double` `res = ` `pow` `(` `ceil` `((` `pow` `(` `pow` `(10, ` ` ` `(n - 1)), 1 / 4) )), 4); ` ` ` `return` `(` `int` `)res; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `n = 1; ` ` ` `cout << (cal(n)); ` `} ` ` ` `// This code is contributed by Mohit Kumar ` |

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## Java

`// Java implementation of the approach ` `class` `GFG ` `{ ` ` ` `// Function to return the smallest n-digit ` `// number which is a perfect fourth power ` `static` `int` `cal(` `int` `n) ` `{ ` ` ` `double` `res = Math.pow(Math.ceil(( ` ` ` `Math.pow(Math.pow(` `10` `, ` ` ` `(n - ` `1` `)), ` `1` `/ ` `4` `) )), ` `4` `); ` ` ` `return` `(` `int` `)res; ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `int` `n = ` `1` `; ` ` ` `System.out.println(cal(n)); ` `} ` `} ` ` ` `// This code is contributed by CodeMech ` |

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## Python3

`# Python3 implementation of the approach ` `from` `math ` `import` `*` ` ` `# Function to return the smallest n-digit ` `# number which is a perfect fourth power ` `def` `cal(n): ` ` ` `res ` `=` `pow` `(ceil( (` `pow` `(` `pow` `(` `10` `, (n ` `-` `1` `)), ` `1` `/` `4` `) ) ), ` `4` `) ` ` ` `return` `int` `(res) ` ` ` `# Driver code ` `n ` `=` `1` `print` `(cal(n)) ` |

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## C#

`// C# implementation of the approach ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to return the smallest n-digit ` `// number which is a perfect fourth power ` `static` `int` `cal(` `int` `n) ` `{ ` ` ` `double` `res = Math.Pow(Math.Ceiling(( ` ` ` `Math.Pow(Math.Pow(10, ` ` ` `(n - 1)), 1 / 4) )), 4); ` ` ` `return` `(` `int` `)res; ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main() ` `{ ` ` ` `int` `n = 1; ` ` ` `Console.Write(cal(n)); ` `} ` `} ` ` ` `// This code is contributed ` `// by Akanksha_Rai ` |

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**Output:**

1

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