Submitted by **DryEstablishment2** t3_zy4vh0
in **explainlikeimfive**

Like for example on websites like Wolfram Alpha you can compute crazy numbers like 2838393^72829 and it gives you a huge decimal approximation for it. Obviously when it’s simple maths it’s easy to do, but how they even calculate numbers like these quickly and correctly?! It blows my mind?!

AquaRegiat1_j23slck wroteThere are often shortcuts that can be used to make the problem easier. For example the fact that:

>(x^(a))^(b) = x^(ab)

Using this knowledge you can break down the exponent in your example, by finding its factors:

>67 * 1087 = 72829

1087 is still a bit large, so we can use another trick:

>x^(a) * x^(b) = x^(a+b)

And for example break it down to:

>500 + 587 = 1087

Using all this we can then perform the calculation:

>(2838393^(500) * 2838393^(587))^(67)

Which is a lot less daunting. It could probably use other rules to break it down further, but this is the general concept.