SOLUTION: What is the simplest form of the expression (x/y)^4 over (x^8/y^11)? Which answer is it? a. y^4/x^7 b. y^7/x^4 c. x^4/y^7 d. x^7/y^4

Algebra ->  Exponents -> SOLUTION: What is the simplest form of the expression (x/y)^4 over (x^8/y^11)? Which answer is it? a. y^4/x^7 b. y^7/x^4 c. x^4/y^7 d. x^7/y^4      Log On


   

Question 633388: What is the simplest form of the expression (x/y)^4 over (x^8/y^11)?
Which answer is it?
a. y^4/x^7
b. y^7/x^4
c. x^4/y^7
d. x^7/y^4
Answer by dfrazzetto(283) About Me  (Show Source):
You can put this solution on YOUR website!
(x/y)^4 over (x^8/y^11)
%28x%5E4%2Fy%5E4%29+%2F+%28x%5E8%2Fy%5E11%29
%28x%5E4+%2A+y%5E11%29+%2F+%28x%5E8+%2A+y%5E4%29
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: %28x%5E4%2Fy%5E4%29%2F%28x%5E8%2Fy%5E11%29 simplifies to y%5E%287%29%2Fx%5E4
  • Text form: (x^4/y^4)/(x^8/y^11) simplifies to y^(7)/x^4
  • Cartoon (animation) form: simplify_cartoon%28+%28x%5E4%2Fy%5E4%29%2F%28x%5E8%2Fy%5E11%29+%29
    For tutors: simplify_cartoon( (x^4/y^4)/(x^8/y^11) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28highlight_red%28+x%5E4%2Fy%5E4+%29%29%2F%28x%5E8%2Fy%5E11%29+%29.
Remove unneeded parentheses around factor highlight_red%28+x%5E4+%29,highlight_red%28+1%2Fy%5E4+%29
It becomes highlight_green%28+x%5E4+%29%2Fhighlight_green%28+y%5E4+%29%2F%28x%5E8%2Fy%5E11%29.
Look at highlight_red%28+x%5E4%2Fy%5E4%2F%28highlight_red%28+x%5E8%2Fy%5E11+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+1%2Fx%5E8+%29,highlight_red%28+y%5E11+%29
It becomes x%5E4%2Fy%5E4%2Fhighlight_green%28+x%5E8+%29%2Ahighlight_green%28+y%5E11+%29.
Look at highlight_red%28+x%5E4+%29%2Fy%5E4%2Fhighlight_red%28+x%5E8+%29%2Ay%5E11.
Reduce similar several occurrences of highlight_red%28+x%5E4+%29 to highlight_green%28+x%5E%284-8%29+%29
It becomes highlight_green%28+x%5E%284-8%29+%29%2Fy%5E4%2Ay%5E11.
Look at x%5E%284-8%29%2Fhighlight_red%28+y%5E4+%29%2Ahighlight_red%28+y%5E11+%29.
Reduce similar several occurrences of highlight_red%28+1%2Fy%5E4+%29 to highlight_green%28+y%5E%28-4%2B11%29+%29
It becomes x%5E%284-8%29%2Ahighlight_green%28+y%5E%28-4%2B11%29+%29.
Look at x%5E%28highlight_red%28+4+%29-highlight_red%28+8+%29%29%2Ay%5E%28-4%2B11%29.
Added fractions or integers together
It becomes x%5E%28highlight_green%28+-4+%29%29%2Ay%5E%28-4%2B11%29.
Look at x%5E%28-4%29%2Ay%5E%28-highlight_red%28+4+%29%2Bhighlight_red%28+11+%29%29.
Added fractions or integers together
It becomes x%5E%28-4%29%2Ay%5E%28highlight_green%28+7+%29%29.
Look at x%5E%28highlight_red%28+-4+%29%29%2Ay%5E%287%29.
Removed extra sign in front of -4
It becomes x%5E%28-highlight_green%28+4+%29%29%2Ay%5E%287%29.
Look at highlight_red%28+x%5E%28-4%29+%29%2Ay%5E%287%29.
Negative power changes multiplication to division
It becomes 1%2Fhighlight_green%28+x%5E4+%29%2Ay%5E%287%29.
Look at highlight_red%28+1+%29%2Fx%5E4%2Ay%5E%287%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes y%5E%287%29%2Fx%5E4.
Result: y%5E%287%29%2Fx%5E4

Universal Simplifier and Solver


Done!


y^7 / x^4, answer b