Algebra please please help

Question

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

How do I do this?

Answer 1

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

 

Answer 2

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) = (3^2-3x^8-14) = 3^-1x^-6 = 1/(3x⁶)

Either bolded expression should be acceptable.

Answer 3

      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