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Write in simplest form.9x^8/27x^14

How do I do this?

9x8 = (3)(3)(x)(x)(x)(x)(x)(x)(x)(x)

27x14 = (3)(3)(3)(x)(x)(x)(x)(x)(x)(x)(x)(x)(x)(x)(x)(x)(x)

The (3)(3)/(3)(3)(3) reduces to give you 1/3, the x's reduce to give you 1/x6 . Multiplying the two together, and you get 1/3x6

Exponents are your friends and you should embrace them. Get rid of the division sign by using negative exponents. From there, you combine exponents by adding them. That is:

(9x8)/(27x14) = (32x8)(3-3x-14) = (32-3x8-14) = 3-1x-6 = 1/(3x6)

Either bolded expression should be acceptable.

1   9 X X X X X X X X
27 X X X X X X X X X X X X X X
3

To perform this division, you are removing any common factors from both your numerator and denominator.  Using the illustration above, you can remove 9 from both the numerator and the denominator leaving 1 in the numerator and 3 in the denominator.  (The reason you can do this is because you can divide any number by one without changing its value.  9/9 is 1)

You can do the same with the variable x.  leaving you with no x's in the numerator and 5 in the denominator.  So your answer is
1
3 x6