SOLUTION: Simplify (-2*x^3)^2 * x * (3*x^-2)

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Question 282259: Simplify (-2*x^3)^2 * x * (3*x^-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: %28-2%2Ax%5E3%29%5E2%2Ax%2A%283%2Ax%5E-2%29 simplifies to 12%2Ax%5E5
  • Text form: (-2*x^3)^2*x*(3*x^-2) simplifies to 12*x^5
  • Cartoon (animation) form: simplify_cartoon%28+%28-2%2Ax%5E3%29%5E2%2Ax%2A%283%2Ax%5E-2%29+%29
    For tutors: simplify_cartoon( (-2*x^3)^2*x*(3*x^-2) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28-2%2Ax%5E3%29%5E2%2Ax%2A%28highlight_red%28+3%2Ax%5E-2+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+3+%29,highlight_red%28+x%5E-2+%29
It becomes %28-2%2Ax%5E3%29%5E2%2Ax%2Ahighlight_green%28+3+%29%2Ahighlight_green%28+x%5E-2+%29.
Look at %28-2%2Ax%5E3%29%5E2%2Ahighlight_red%28+x+%29%2A3%2Ahighlight_red%28+x%5E-2+%29.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E%281%2B-2%29+%29
It becomes %28-2%2Ax%5E3%29%5E2%2Ahighlight_green%28+x%5E%281%2B-2%29+%29%2A3.
Look at %28-2%2Ax%5E3%29%5E2%2Ax%5E%281%2Bhighlight_red%28+-2+%29%29%2A3.
Removed extra sign in front of -2
It becomes %28-2%2Ax%5E3%29%5E2%2Ax%5E%281-highlight_green%28+2+%29%29%2A3.
Look at %28-2%2Ax%5E3%29%5E2%2Ax%5E%28highlight_red%28+1+%29-highlight_red%28+2+%29%29%2A3.
Added fractions or integers together
It becomes %28-2%2Ax%5E3%29%5E2%2Ax%5E%28highlight_green%28+-1+%29%29%2A3.
Look at %28-2%2Ax%5E3%29%5E2%2Ax%5E%28highlight_red%28+-1+%29%29%2A3.
Removed extra sign in front of -1
It becomes %28-2%2Ax%5E3%29%5E2%2Ax%5E%28-highlight_green%28+1+%29%29%2A3.
Look at %28-2%2Ax%5E3%29%5E2%2Ahighlight_red%28+x%5E%28-1%29+%29%2A3.
Negative power changes multiplication to division
It becomes %28-2%2Ax%5E3%29%5E2%2Fhighlight_green%28+x%5E1+%29%2A3.
Look at %28-2%2Ax%5E3%29%5E2%2Fx%5Ehighlight_red%28+1+%29%2A3.
Removing power of one highlight_red%28+1+%29
Look at highlight_red%28+%28-2%2Ax%5E3%29%5E2+%29%2Fhighlight_red%28+x+%29%2A3.
Canceled out common factors (x-(0))
Look at highlight_red%28+%28highlight_red%28+4%2Ax%5E5+%29%29%2F%281%29%2A3+%29.
Remove unneeded parentheses around factor highlight_red%28+4+%29,highlight_red%28+x%5E5+%29
It becomes highlight_green%28+4+%29%2Ahighlight_green%28+x%5E5+%29%2F%281%29%2A3.
Look at highlight_red%28+4%2Ax%5E5%2F%28highlight_red%28+1+%29%29%2A3+%29.
Remove unneeded parentheses around factor highlight_red%28+1%2F1+%29
It becomes 4%2Ax%5E5%2Fhighlight_green%28+1+%29%2A3.
Look at highlight_red%28+4+%29%2Ax%5E5%2F1%2Ahighlight_red%28+3+%29.
Multiplied numerator integers
It becomes highlight_green%28+12+%29%2Ax%5E5%2F1.
Look at 12%2Ax%5E5%2Fhighlight_red%28+1+%29.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 12%2Ax%5E5.
Result: 12%2Ax%5E5

Universal Simplifier and Solver


Done!


So
(-2*x^3)^2*x*(3*x^-2) simplifies to 12*x^5 and bob's your uncle!