write in simplest form. 2x^8over 8x^17 or 2x^8/8x^17?

Question

please show me how to work this problem

Answer 1

OK, the 2/8 simplifies to 1/4. To simplify the x^8/x^17, just subtract the denominator's exponent from the numerator's exponent. This would be 8-17 = -9. This becomes x's new exponent, making it x^-9. So putting the 1/4 back in with the x^-9, we get (x^-9)/4.

EDIT: This answer is the same as hemi's answer of 1/(4x^9) shown below, but this answer is simplified more. A negative exponent in the numerator becomes positive in the denominator, and vice versa. Going back and forth from denominator to numerator changes the sign of the exponent.
For example, 1/x = x^-1 and 1/(X^-1) = x.

Answer 2

(2x^8)/(8x^17): simplify (2/8) and subtract exponents for the x's:
(2/8) = 1/4 and 17 - 8 = 9, since the 17 is in the denominator, the 9 will also be, so you have 1/(4x^9).
This works because the numerator is really 2xxxxxxxx. x^8 is an abbreviation for 8 x's multiplied together. The denominator is 8 times 17 x's multiplied together.
The 2 and the 8 have a common factor of 2, so we can cancel 2 from the numerator and the denominator. How many x's can we cancel? Well, 8 is smaller than 17, so we can cancel 8 x's. When we do that, all the x's in the numerator are gone and in the denominator, there are 17 - 8 = 9 left.

Answer 3

= 2x^8 / 8x^17
= (1/4) x^(- 9)
= 1 / (4 x^9)

Answer 4

1/(4x^9)