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

How do I do this?

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

How do I do this?

Tutors, please sign in to answer this question.

Find common factors between your numerator and your denominator

9x^{8} = (3)(3)(x)(x)(x)(x)(x)(x)(x)(x)

27x^{14} = (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/x^{6} . Multiplying the two together, and you get 1/3x^{6}

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:

(9x^{8})/(27x^{14}) = (3^{2}x^{8})(3^{-3}x^{-14}) = (3^{2-3}x^{8-14}) =
**3 ^{-1}x^{-6}** =

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 x^{6}