# What is 405 to the 3rd Power?

So you want to know what 405 to the 3rd power is do you? In this article we'll explain exactly how to perform the mathematical operation called "the exponentiation of 405 to the power of 3". That might sound fancy, but we'll explain this with no jargon! Let's do it.

## What is an Exponentiation?

Let's get our terms nailed down first and then we can see how to work out what 405 to the 3rd power is.

When we talk about exponentiation all we really mean is that we are multiplying a number which we call the *base* (in this case 405) by itself a certain number of times. The *exponent* is the number of times to multiply 405 by itself, which in this case is 3 times.

## 405 to the Power of 3

There are a number of ways this can be expressed and the most common ways you'll see 405 to the 3rd shown are:

- 405
^{3} - 405^3

So basically, you'll either see the exponent using superscript (to make it smaller and slightly above the base number) or you'll use the caret symbol (^) to signify the exponent. The caret is useful in situations where you might not want or need to use superscript.

So we mentioned that exponentation means multiplying the base number by itself for the exponent number of times. Let's look at that a little more visually:

405 to the 3rd Power = 405 x ... x 405 (3 times)

## So What is the Answer?

Now that we've explained the theory behind this, let's crunch the numbers and figure out what 405 to the 3rd power is:

405 to the power of 3 = 405^{3} = 66,430,125

Why do we use exponentiations like 405^{3} anyway? Well, it makes it much easier for us to write multiplications and conduct mathematical operations with both large and small numbers when you are working with numbers with a lot of trailing zeroes or a lot of decimal places.

Hopefully this article has helped you to understand how and why we use exponentiation and given you the answer you were originally looking for. Now that you know what 405 to the 3rd power is you can continue on your merry way.

Feel free to share this article with a friend if you think it will help them, or continue on down to find some more examples.

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