Missing Base Finder

Enter the exponent and result to quickly find the base.

Calculate the Missing Base: ?n = V

Result

How to Calculate the Base?

An exponent is a mathematical expression that represents how many times a number (the base) is multiplied by itself. So, when you know the exponent and the result, you can calculate the missing base using a root operation. The process involves solving the equation \( a^n = V \), where \( a \) is the base, \( n \) is the exponent, and \( V \) is the result.

Steps to Calculate the Base

  1. Identify the exponent and the result: Let \( n \) represent the exponent and \( V \) represent the result.
  2. Apply the formula to find the base: \( a = \sqrt[n]{V} \)

Examples

Example 1: Find the missing base when \( n = 3 \) and \( V = 64 \).

Solution:

Exponent: \( n = 3 \), Result: \( V = 64 \)

Use the formula:

\( a = \sqrt[3]{64} \)

Calculate the base:

\( a = 4 \)

Conclusion: The missing base is \( 4 \), since \( 4^3 = 64 \).

Example 2: Find the missing base when \( n = 4 \) and \( V = 81 \).

Solution:

Exponent: \( n = 4 \), Result: \( V = 81 \)

Use the formula:

\( a = \sqrt[4]{81} \)

Calculate the base:

\( a = 3 \)

Conclusion: The missing base is \( 3 \), since \( 3^4 = 81 \).

Example 3: Find the missing base when \( n = 5 \) and \( V = 243 \).

Solution:

Exponent: \( n = 5 \), Result: \( V = 243 \)

Use the formula:

\( a = \sqrt[5]{243} \)

Calculate the base:

\( a = 3 \)

Conclusion: The missing base is \( 3 \), since \( 3^5 = 243 \).