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Algebra please please help

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

How do I do this?

3 Answers by Expert Tutors

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Kevin S. |
5.0 5.0 (4 lesson ratings) (4)

Find common factors between your numerator and your denominator

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


Brian C. | Advanced Math and Science TutorAdvanced Math and Science Tutor
4.5 4.5 (173 lesson ratings) (173)

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.

Mary K. | Math and Computer Science Tutor/ Microsoft Certified Word and ExcelMath and Computer Science Tutor/ Microso...
5.0 5.0 (106 lesson ratings) (106)

      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

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
   3 x6