Exponent Calculator

Calculate powers, roots, solve for exponent or base, and convert decimal numbers to scientific notation with this exponent calculator.

• All Math and Numbers Calculators
• 10th Power Calculator
• e^x Calculator
• Exp Calculator
• Reverse Exponent Calculator
• Natural Log Calculator
• Log Base 2 Calculator

Exponents Formula

The following formula is used to calculate an exponent.

• Where X and Y are variables
• n is the exponent

Exponent Definition

In Xⁿ = Y, X is the base and n is the exponent. A positive integer exponent indicates repeated multiplication: 2² = 2 × 2 = 4 and 3⁴ = 3 × 3 × 3 × 3 = 81. Negative exponents give reciprocals, while fractional exponents relate to roots on their real-number domains.

How to calculate an exponent?

The following example is similar to the ones described in the section above. This example will follow the calculation given the variable x and exponent n.

1. The first step is to determine the values of both X and n. In this case, we will assume x=5 and n=3.
2. The next step is to set up the factor equation to solve for Y. This equation should look like the following: 5³ = Y.
3. The final step is to multiply 5 by itself 3 times, so 5*5*5 = 125.

This next example will show you how to calculate the exponent given the original variable X and the final value Y.

1. In this example let’s assume X = 8 and Y = 64.
2. The first step is to understand that a logarithm is the inverse of an exponent. Therefore, the exponent can be calculated using the log of Y with a base of X.
3. Finally solve n = ln(64) / ln(8) = 2. This logarithmic inverse requires X > 0, X ≠ 1 and Y > 0.

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