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}

Dr. Anthon S.

Best Results By Perfect Score SAT/ACT Tutor! Math, Physics and more!

New York, NY

5.0
(456 ratings)

Nikunj P.

Math and Science Specialist, Over 14 Years of Educational Experience

Scarsdale, NY

4.9
(163 ratings)

David T.

Very Experienced, Knowledgeable, and Patient Math Tutor

Dobbs Ferry, NY

5.0
(93 ratings)