SOLUTION: can anyone show me how to simplify this problem without negative exponents? {{{ ( x*y^5 / x^-4y^2 )^-2 }}}

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Question 289435: can anyone show me how to simplify this problem without negative exponents? ++%28+x%2Ay%5E5+%2F+x%5E-4y%5E2+%29%5E-2+
Answer by Deina(147) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: %28x%2Ay%5E5%2Fx%5E%28-4%29%2Ay%5E2%29%5E%28-2%29 simplifies to 1%2F%28x%5E%285%29%2Ay%5E%287%29%29%5E2
  • Text form: (x*y^5/x^(-4)*y^2)^(-2) simplifies to 1/(x^(5)*y^(7))^2
  • Cartoon (animation) form: simplify_cartoon%28+%28x%2Ay%5E5%2Fx%5E%28-4%29%2Ay%5E2%29%5E%28-2%29+%29
    For tutors: simplify_cartoon( (x*y^5/x^(-4)*y^2)^(-2) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at %28highlight_red%28+x+%29%2Ay%5E5%2Fhighlight_red%28+x%5E%28-4%29+%29%2Ay%5E2%29%5E%28-2%29.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E%281-%28-4%29%29+%29
It becomes %28highlight_green%28+x%5E%281-%28-4%29%29+%29%2Ay%5E5%2Ay%5E2%29%5E%28-2%29.
Look at .
Reduce similar several occurrences of highlight_red%28+y%5E5+%29 to highlight_green%28+y%5E%285%2B2%29+%29
It becomes %28x%5E%281-%28-4%29%29%2Ahighlight_green%28+y%5E%285%2B2%29+%29%29%5E%28-2%29.
Look at %28x%5E%281-highlight_red%28+%28-4%29+%29%29%2Ay%5E%285%2B2%29%29%5E%28-2%29.
Removed extra sign in front of 4
It becomes %28x%5E%281%2Bhighlight_green%28+4+%29%29%2Ay%5E%285%2B2%29%29%5E%28-2%29.
Look at %28x%5E%28highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%29%2Ay%5E%285%2B2%29%29%5E%28-2%29.
Added fractions or integers together
It becomes %28x%5E%28highlight_green%28+5+%29%29%2Ay%5E%285%2B2%29%29%5E%28-2%29.
Look at %28x%5E%285%29%2Ay%5E%28highlight_red%28+5+%29%2Bhighlight_red%28+2+%29%29%29%5E%28-2%29.
Added fractions or integers together
It becomes %28x%5E%285%29%2Ay%5E%28highlight_green%28+7+%29%29%29%5E%28-2%29.
Look at highlight_red%28+%28x%5E%285%29%2Ay%5E%287%29%29%5E%28-2%29+%29.
Negative power changes multiplication to division
It becomes 1%2Fhighlight_green%28+%28x%5E%285%29%2Ay%5E%287%29%29%5E2+%29.
Result: 1%2F%28x%5E%285%29%2Ay%5E%287%29%29%5E2

Universal Simplifier and Solver


Done!
and bob's your uncle!