# Power Function Calculator

Created by Arturo Barrantes
Reviewed by Luis Hoyos
Last updated: Jun 05, 2023

Table of contents:

The power function calculator helps you obtain any number to the power of positive, negative, zero, or even decimal exponents. In this article, we will cover what is a power function in math and explore several examples, even extreme cases such as what is 2 to the power of 30.

## What is a power function in math?

A power function is a math function where you have a base, and an exponent in the following formula:

$f(x) = x^n$

, where x represents the base, n is the exponent, and f(x) is the power function. The exponent indicates how many times we will multiply the base. For example, if somebody asks: What is 2 to the power of 30?. We will have to multiply thirty times the number 2. Sounds like a lot, right?

In such cases, we can use our power function calculator. Consequently, the result is 1,073,741,824. But what if we see a problem requiring 4 to the power of 0 or the power of -2? We are going to cover those and other cases in the next section.

## How to calculate the power of any number?

Regarding calculating the power of any number, we will use the method explained above but separated into three sections:

• When the exponent is positive: We follow the same process indicated above for power functions. Example: 4 to the power of 4: 4 x 4 x 4 x 4 = 256.

• When the exponent is negative: Example: What is 2 to the power of -3.

1. Find out the exponent. In this case: -3. Hence, we will use the - to convert the base to its reciprocal.
2. Write the reciprocal of the base. If the base is 2, we use $\frac{1}{2}$.
3. Multiply the new base as many times as the exponent indicates: $\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$.
• When the exponent is 0: Any number to the power of 0 equals 1.

## Other useful tools like the power function calculator

Since you already know how power functions work, you can take a look at other related tools:

## FAQ

### What is anything to the power of 0?

1. As a convention, anything to the power of 0 is 1. So, in case anybody asks what 1 million to the power of 0 is, then you say: simply 1.

### What is 2 to the power of 3?

It is 8. You can use the Omnicalculator's tool: Power function calculator or:

1. Determine the power to which it's raised. In this case, it's 3.
2. Multiply three times the base: 2 * 2 * 2. The result is 8.

### What is 2 million to the power of 0?

Remember, whenever somebody asks you what is anything to the power of 0, the answer is 1.

Arturo Barrantes
f(x) = bx
Base (b)
Exponent (x)
Power Function f(x)
Step-by-step solution
• Let's calculate:
bx = f(x)
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