SOLUTION: how do i simplify the following {{{(3k^2 * m^2) * (4k^3 * m^3)}}}

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Question 214093: how do i simplify the following %283k%5E2+%2A+m%5E2%29+%2A+%284k%5E3+%2A+m%5E3%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: %283k%5E2m%5E2%29%2A%284k%5E3m%5E3%29 simplifies to 12%2Ak%5E%285%29%2Am%5E%285%29
  • Text form: (3k^2m^2)*(4k^3m^3) simplifies to 12*k^(5)*m^(5)
  • Cartoon (animation) form: simplify_cartoon%28+%283k%5E2m%5E2%29%2A%284k%5E3m%5E3%29+%29
    For tutors: simplify_cartoon( (3k^2m^2)*(4k^3m^3) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28highlight_red%28+3%2Ak%5E2%2Am%5E2+%29%29%2A%284%2Ak%5E3%2Am%5E3%29+%29.
Remove unneeded parentheses around factor highlight_red%28+3+%29,highlight_red%28+k%5E2+%29,highlight_red%28+m%5E2+%29
It becomes .
Look at highlight_red%28+3%2Ak%5E2%2Am%5E2%2A%28highlight_red%28+4%2Ak%5E3%2Am%5E3+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+4+%29,highlight_red%28+k%5E3+%29,highlight_red%28+m%5E3+%29
It becomes .
Look at highlight_red%28+3+%29%2Ak%5E2%2Am%5E2%2Ahighlight_red%28+4+%29%2Ak%5E3%2Am%5E3.
Multiplied numerator integers
It becomes highlight_green%28+12+%29%2Ak%5E2%2Am%5E2%2Ak%5E3%2Am%5E3.
Look at 12%2Ahighlight_red%28+k%5E2+%29%2Am%5E2%2Ahighlight_red%28+k%5E3+%29%2Am%5E3.
Reduce similar several occurrences of highlight_red%28+k%5E2+%29 to highlight_green%28+k%5E%282%2B3%29+%29
It becomes 12%2Ahighlight_green%28+k%5E%282%2B3%29+%29%2Am%5E2%2Am%5E3.
Look at 12%2Ak%5E%282%2B3%29%2Ahighlight_red%28+m%5E2+%29%2Ahighlight_red%28+m%5E3+%29.
Reduce similar several occurrences of highlight_red%28+m%5E2+%29 to highlight_green%28+m%5E%282%2B3%29+%29
It becomes 12%2Ak%5E%282%2B3%29%2Ahighlight_green%28+m%5E%282%2B3%29+%29.
Look at 12%2Ak%5E%28highlight_red%28+2+%29%2Bhighlight_red%28+3+%29%29%2Am%5E%282%2B3%29.
Added fractions or integers together
It becomes 12%2Ak%5E%28highlight_green%28+5+%29%29%2Am%5E%282%2B3%29.
Look at 12%2Ak%5E%285%29%2Am%5E%28highlight_red%28+2+%29%2Bhighlight_red%28+3+%29%29.
Added fractions or integers together
It becomes 12%2Ak%5E%285%29%2Am%5E%28highlight_green%28+5+%29%29.
Result: 12%2Ak%5E%285%29%2Am%5E%285%29

Universal Simplifier and Solver


Done!