document.write( "Question 282259: Simplify (-2*x^3)^2 * x * (3*x^-2) \n" ); document.write( "

Algebra.Com's Answer #205663 by Deina(147) $\"\"$ $\"About$

You can put this solution on YOUR website!
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

\n" ); document.write( "
\n" ); document.write( "

\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

\n" ); document.write( "\n" ); document.write( "

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.

\n" ); document.write( "

DETAILED EXPLANATION

\n" ); document.write( "

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 $\"%28-2%2Ax%5E3%29%5E2%2Ax%2Ahighlight_green%28+3+%29%2Ahighlight_green%28+x%5E-2+%29\"$ .
\n" ); document.write( "

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 $\"%28-2%2Ax%5E3%29%5E2%2Ahighlight_green%28+x%5E%281%2B-2%29+%29%2A3\"$ .
\n" ); document.write( "

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 $\"%28-2%2Ax%5E3%29%5E2%2Ax%5E%281-highlight_green%28+2+%29%29%2A3\"$ .
\n" ); document.write( "

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 $\"%28-2%2Ax%5E3%29%5E2%2Ax%5E%28highlight_green%28+-1+%29%29%2A3\"$ .
\n" ); document.write( "

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 $\"%28-2%2Ax%5E3%29%5E2%2Ax%5E%28-highlight_green%28+1+%29%29%2A3\"$ .
\n" ); document.write( "

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 $\"%28-2%2Ax%5E3%29%5E2%2Fhighlight_green%28+x%5E1+%29%2A3\"$ .
\n" ); document.write( "

Look at $\"%28-2%2Ax%5E3%29%5E2%2Fx%5Ehighlight_red%28+1+%29%2A3\"$ .
Removing power of one $\"highlight_red%28+1+%29\"$
\n" ); document.write( "

Look at $\"highlight_red%28+%28-2%2Ax%5E3%29%5E2+%29%2Fhighlight_red%28+x+%29%2A3\"$ .
Canceled out common factors (x-(0))
\n" ); document.write( "

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 $\"highlight_green%28+4+%29%2Ahighlight_green%28+x%5E5+%29%2F%281%29%2A3\"$ .
\n" ); document.write( "

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 $\"4%2Ax%5E5%2Fhighlight_green%28+1+%29%2A3\"$ .
\n" ); document.write( "

Look at $\"highlight_red%28+4+%29%2Ax%5E5%2F1%2Ahighlight_red%28+3+%29\"$ .
Multiplied numerator integers
It becomes $\"highlight_green%28+12+%29%2Ax%5E5%2F1\"$ .
\n" ); document.write( "

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: $\"12%2Ax%5E5\"$
\n" ); document.write( "

Universal Simplifier and Solver

\n" ); document.write( "
Done!

\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So
\n" ); document.write( "(-2*x^3)^2*x*(3*x^-2) simplifies to 12*x^5 and bob's your uncle!
\n" ); document.write( " \n" ); document.write( "

\n" );