SOLUTION: simplify the expression, please. {{{r^(-3)*s^5*t^2/r^2/s/t^(-2)}}}

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: simplify the expression, please. {{{r^(-3)*s^5*t^2/r^2/s/t^(-2)}}}      Log On


   

Question 5839: simplify the expression, please.
r%5E%28-3%29%2As%5E5%2At%5E2%2Fr%5E2%2Fs%2Ft%5E%28-2%29
Answer by ichudov(507) 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: r%5E%28-3%29%2As%5E5%2At%5E2%2Fr%5E2%2Fs%2Ft%5E%28-2%29 simplifies to s%5E%284%29%2Fr%5E5%2At%5E%284%29
  • Text form: r^(-3)*s^5*t^2/r^2/s/t^(-2) simplifies to s^(4)/r^5*t^(4)
  • Cartoon (animation) form: simplify_cartoon%28+r%5E%28-3%29%2As%5E5%2At%5E2%2Fr%5E2%2Fs%2Ft%5E%28-2%29+%29
    For tutors: simplify_cartoon( r^(-3)*s^5*t^2/r^2/s/t^(-2) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Reduce similar several occurrences of highlight_red%28+r%5E%28-3%29+%29 to highlight_green%28+r%5E%28%28-3%29-2%29+%29
It becomes highlight_green%28+r%5E%28%28-3%29-2%29+%29%2As%5E5%2At%5E2%2Fs%2Ft%5E%28-2%29.
Look at .
Reduce similar several occurrences of highlight_red%28+s%5E5+%29 to highlight_green%28+s%5E%28-1%2B5%29+%29
It becomes r%5E%28%28-3%29-2%29%2Ahighlight_green%28+s%5E%28-1%2B5%29+%29%2At%5E2%2Ft%5E%28-2%29.
Look at .
Reduce similar several occurrences of highlight_red%28+t%5E2+%29 to highlight_green%28+t%5E%282-%28-2%29%29+%29
It becomes r%5E%28%28-3%29-2%29%2As%5E%28-1%2B5%29%2Ahighlight_green%28+t%5E%282-%28-2%29%29+%29.
Look at r%5E%28highlight_red%28+%28-3%29+%29-2%29%2As%5E%28-1%2B5%29%2At%5E%282-%28-2%29%29.
Removed extra sign in front of -3
It becomes r%5E%28-highlight_green%28+3+%29-2%29%2As%5E%28-1%2B5%29%2At%5E%282-%28-2%29%29.
Look at r%5E%28-3-2%29%2As%5E%28highlight_red%28+-1+%29%2B5%29%2At%5E%282-%28-2%29%29.
Removed extra sign in front of -1
It becomes r%5E%28-3-2%29%2As%5E%28-highlight_green%28+1+%29%2B5%29%2At%5E%282-%28-2%29%29.
Look at r%5E%28-3-2%29%2As%5E%28-1%2B5%29%2At%5E%282-highlight_red%28+%28-2%29+%29%29.
Removed extra sign in front of 2
It becomes r%5E%28-3-2%29%2As%5E%28-1%2B5%29%2At%5E%282%2Bhighlight_green%28+2+%29%29.
Look at .
Added fractions or integers together
It becomes r%5E%28highlight_green%28+-5+%29%29%2As%5E%28-1%2B5%29%2At%5E%282%2B2%29.
Look at r%5E%28-5%29%2As%5E%28-highlight_red%28+1+%29%2Bhighlight_red%28+5+%29%29%2At%5E%282%2B2%29.
Added fractions or integers together
It becomes r%5E%28-5%29%2As%5E%28highlight_green%28+4+%29%29%2At%5E%282%2B2%29.
Look at r%5E%28-5%29%2As%5E%284%29%2At%5E%28highlight_red%28+2+%29%2Bhighlight_red%28+2+%29%29.
Added fractions or integers together
It becomes r%5E%28-5%29%2As%5E%284%29%2At%5E%28highlight_green%28+4+%29%29.
Look at r%5E%28highlight_red%28+-5+%29%29%2As%5E%284%29%2At%5E%284%29.
Removed extra sign in front of -5
It becomes r%5E%28-highlight_green%28+5+%29%29%2As%5E%284%29%2At%5E%284%29.
Look at highlight_red%28+r%5E%28-5%29+%29%2As%5E%284%29%2At%5E%284%29.
Negative power changes multiplication to division
It becomes 1%2Fhighlight_green%28+r%5E5+%29%2As%5E%284%29%2At%5E%284%29.
Look at highlight_red%28+1+%29%2Fr%5E5%2As%5E%284%29%2At%5E%284%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes s%5E%284%29%2Fr%5E5%2At%5E%284%29.
Result: s%5E%284%29%2Fr%5E5%2At%5E%284%29

Universal Simplifier and Solver


Done!