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Suppose you have (x5)(x6); Just remember that you're counting factors.

x5 = (x)(x)(x)(x)(x) and x6 = (x)(x)(x)(x)(x)(x)

Now multiply them together:

(x5)(x6) = (x)(x)(x)(x)(x)(x)(x)(x)(x)(x)(x) = x11

Why x11? Well, how many x's are there? Five x factors from x5, and six x factors from x6, makes 11 x factors total.

Can you see that whenever you multiply any two powers of the same base, you end up with a number of factors equal to the total of the two powers? In other words, when the bases are the same, you find the new power by just adding the exponents:

Q: What are the laws of exponent multiplication?

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Exponent is repeated multiplication

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An exponent of 1 can be ignored. In the same way that multiplication by 1 can be ignored.

The exponent for a factor is the number of times that the factor appras in the multiplication. An exponent of 1 is not usually written out. So, 2*2*2*3*3*3*3*5 = 23*34*5

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Because it is derived so easily from simple multiplication and division of variables. It is so very intuitive. Multiply x by x and you have x2 do it again and it's cubed etc.