# Exponent Arithmetic

Starting points, what the symbols mean :

Fractional exponents are a way to represent roots :

If w^{2} = s, then w = s^{1/2} That is, a 1/2 exponent is another way to write square
root.

The nice thing about exponents is that you can do many
calculations without using your

calculator , and in science we express many quantities as powers of ten .

In multiplication , add exponents when the same number (in the case shown, 10) is raised to a power:

In division , subtract exponents when the same number (in the case shown, 10) is raised to a power:

When raising to a power , multiply . When taking a root , divide as shown below:

Problems for practice:

I have intentionally set up the following problems so you could solve them
without a

calculator if you apply the rules above . Please try solving these in your head
or use a piece of paper.

If you use a calculator , you are defeating the purpose of the exercise.

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