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Power Function Calculator

Created by Arturo Barrantes
Reviewed by Luis Hoyos
Last updated: Jan 18, 2024


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)=xnf(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 12\frac{1}{2}.
    3. Multiply the new base as many times as the exponent indicates: 12Γ—12Γ—12=18\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
β€’ Let's calculate:
bx = f(x)
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