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    Laws of Exponents - Math is Fun

    Writing all the letters down is the key to understanding the Laws So, when in doubt, just remember to write down all the letters (as many as the exponent tells you to) and see if you can make sense of it.

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    The "Laws of Exponents" (also called "Rules of Exponents") come from three ideas: If you understand those, then you understand exponents! And all the laws below are based on those ideas.

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    The first three laws above (x1 = x, x0 = 1 and x-1 = 1/x) are just part of the natural sequence of exponents. Have a look at this: Look at that table for a while ... notice that positive, zero or negative exponents are really part of the same pattern, i.e. 5 times larger (or 5 times smaller) depending on whether the exponent gets larger (or smaller...

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    With xmxn, how many times do we end up multiplying "x"? Answer: first "m" times, then by another"n" times, for a total of "m+n" times.

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    Like the previous example, how many times do we end up multiplying "x"? Answer: "m" times, then reduce thatby "n" times (because we are dividing), for a total of "m-n" times. (Remember that x/x = 1, so every time you see an x"above the line" and one "below the line" you can cancel them out.) This law can also show you why x0=1:

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