How to Calculate Exponents
Exponentiation multiplies a base number by itself a specified number of times. It is the foundation for exponential growth and scientific notation.
The Formula
a^n = a x a x ... x a (n times)Where:
aBase — The number being multipliednExponent — How many times to multiply the basea^nPower — The resulting valueStep-by-Step Example
Here's how to calculate exponents step by step:
- 1Identify base and exponent: Find the base number and the power it is raised to.
- 2Multiply repeatedly: Multiply the base by itself the number of times indicated by the exponent.
- 3Apply sign rules: A negative base with an even exponent gives a positive result.
Following these 3 steps gives you the final exponents value.
Skip the Math
Bacteria doubling every hour can be modeled as 2^n, where n is hours. After 10 hours you have 2^10 = 1,024 bacteria.
Use the Free CalculatorWhy You Need This Calculation
- Exponents power compound interest, population growth, computer science, and scientific notation calculations.
Common Mistakes
Multiplying base by exponent instead of repeating.
2^3 is 8 (2x2x2), not 6 (2x3).
Ignoring negative base sign rules.
(-2)^2 = 4 but -2^2 = -4 due to order of operations.
Forgetting that any number to the 0 power is 1.
a^0 = 1 for any non-zero a.