Using exponents is a short way of saying “multiply the number by itself.” The little number up above tells you how many times to multiply the number by itself. So 10^{2} means 10 x 10, or 100. We call this “10 squared” because if you wanted to find the area of a square whose sides were 10 inches long, you’d have to multiply 10 x 10 to get 100 square inches.

How many times would you have to fold a piece of paper to get to the Moon?

In the same way, 10^{3} means 10 x 10 x 10, or 1000. (Each time you have an exponent of 10, the little number up above tells you how many zeros there will be in the answer). We call this 10 cubed, because if you wanted to find the volume of a cube whose sides were 10 inches long, you’d have to multiply 10 x 10 x 10 to get 1000 cubic inches.

Exponents also work with other numbers besides 10. If your square was only 4 inches on a side, you’d find the area by calculating 4^{2}, or 4 x 4= 16 square inches. To find the area of a cube 4 inches on a side, you’d calculate 4^{3}, or 4 x 4 x 4 = 64 cubic inches.

Now you can understand two very big numbers that people sometimes talk about. One is a googol. A googol is 10^{100}, which means 10 x 10 a hundred times (It was actually a nine-year-old boy who came up with the name). A googol is a large number – 1 with a hundred zeroes after it. It’s so big, that a googol is bigger than the number of sub-atomic particles in the known universe. On the other hand, a googol is smaller than the number of possible different games of chess (about 10120).

The second very big number is called a googolplex (also named by the same kid, Milton Sirotta). A googolplex is 10^{googol}, or 1 with a googol zeroes after it. We can’t even write that many zeroes down, even if all the matter in the Universe was turned into paper. If you wrote two numbers a second, it would take you longer than the age of the universe to write it down.

Even though a googolplex is not really a useful number, it can help you to remember that when you use exponents, you can get to big numbers very quickly. Two is a small number, but 2^{2} is 4, and 2^{3} is 8, and 2^{4} is 16, and 2^{5} is 32, and 2^{6} is 64, and 2^{7} is 128, and so on. It doubles every time you increase the exponent. The higher you go with the exponents, the quicker your number gets bigger.

When you draw exponential numbers on a number plane, you end up with a parabola.

## An Islamic story using exponents

More about Numbers

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