Enter the exponent and result to quickly find 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.
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 \( 4^3 = 64 \).
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 \( 3^4 = 81 \).
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 \( 3^5 = 243 \).