Algebra Solver and Math Simplifier that SHOWS WORK

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YOUR ANSWER


  • Graphical form: %2827%2Aa%5E3%2Ab%29%5E-1%2F3%2F%289%2Aa%5E-2%2Ab%5E2%29%5E-1%2F2 simplifies to b%2Fa%5E5%2F18
  • Text form: (27*a^3*b)^-1/3/(9*a^-2*b^2)^-1/2 simplifies to b/a^5/18
  • Cartoon (animation) form: simplify_cartoon%28+%2827%2Aa%5E3%2Ab%29%5E-1%2F3%2F%289%2Aa%5E-2%2Ab%5E2%29%5E-1%2F2+%29
    For tutors: simplify_cartoon( (27*a^3*b)^-1/3/(9*a^-2*b^2)^-1/2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Multiplied denominator integers
It becomes %2827%2Aa%5E3%2Ab%29%5E-1%2Fhighlight_green%28+6+%29%2F%289%2Aa%5E-2%2Ab%5E2%29%5E-1.
Look at %2827%2Aa%5E3%2Ab%29%5E-1%2F6%2F%289%2Ahighlight_red%28+a%5E-2+%29%2Ab%5E2%29%5E-1.
Negative power changes multiplication to division
It becomes %2827%2Aa%5E3%2Ab%29%5E-1%2F6%2F%289%2Fhighlight_green%28+a%5E2+%29%2Ab%5E2%29%5E-1.
Look at highlight_red%28+%2827%2Aa%5E3%2Ab%29%5E-1+%29%2F6%2F%289%2Fa%5E2%2Ab%5E2%29%5E-1.
Negative power changes multiplication to division
It becomes 1%2Fhighlight_green%28+%2827%2Aa%5E3%2Ab%29%5E1+%29%2F6%2F%289%2Fa%5E2%2Ab%5E2%29%5E-1.
Look at 1%2F%2827%2Aa%5E3%2Ab%29%5E1%2F6%2Fhighlight_red%28+%289%2Fa%5E2%2Ab%5E2%29%5E-1+%29.
Negative power changes multiplication to division
It becomes 1%2F%2827%2Aa%5E3%2Ab%29%5E1%2F6%2Ahighlight_green%28+%289%2Fa%5E2%2Ab%5E2%29%5E1+%29.
Look at highlight_red%28+1+%29%2F%2827%2Aa%5E3%2Ab%29%5E1%2F6%2A%289%2Fa%5E2%2Ab%5E2%29%5E1.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %289%2Fa%5E2%2Ab%5E2%29%5E1%2F%2827%2Aa%5E3%2Ab%29%5E1%2F6.
Look at %289%2Fa%5E2%2Ab%5E2%29%5Ehighlight_red%28+1+%29%2F%2827%2Aa%5E3%2Ab%29%5E1%2F6.
Removing power of one highlight_red%28+1+%29
Look at %289%2Fa%5E2%2Ab%5E2%29%2F%2827%2Aa%5E3%2Ab%29%5Ehighlight_red%28+1+%29%2F6.
Removing power of one highlight_red%28+1+%29
Look at highlight_red%28+%28highlight_red%28+9%2Fa%5E2%2Ab%5E2+%29%29%2F%2827%2Aa%5E3%2Ab%29%2F6+%29.
Remove unneeded parentheses around factor highlight_red%28+9+%29,highlight_red%28+1%2Fa%5E2+%29,highlight_red%28+b%5E2+%29
It becomes .
Look at highlight_red%28+9%2Fa%5E2%2Ab%5E2%2F%28highlight_red%28+27%2Aa%5E3%2Ab+%29%29%2F6+%29.
Remove unneeded parentheses around factor highlight_red%28+1%2F27+%29,highlight_red%28+1%2Fa%5E3+%29,highlight_red%28+1%2Fb+%29
It becomes .
Look at highlight_red%28+9+%29%2Fa%5E2%2Ab%5E2%2Fhighlight_red%28+27+%29%2Fa%5E3%2Fb%2F6.
Factors 9 and 27 have greatest common factor (GCF) of 9. Reducing fraction.
It becomes highlight_green%28+1+%29%2Fa%5E2%2Ab%5E2%2Fhighlight_green%28+3+%29%2Fa%5E3%2Fb%2F6.
Look at 1%2Fa%5E2%2Ab%5E2%2Fhighlight_red%28+3+%29%2Fa%5E3%2Fb%2Fhighlight_red%28+6+%29.
Multiplied denominator integers
It becomes 1%2Fa%5E2%2Ab%5E2%2Fhighlight_green%28+18+%29%2Fa%5E3%2Fb.
Look at 1%2Fhighlight_red%28+a%5E2+%29%2Ab%5E2%2F18%2Fhighlight_red%28+a%5E3+%29%2Fb.
Reduce similar several occurrences of highlight_red%28+1%2Fa%5E2+%29 to highlight_green%28+a%5E%28-2-3%29+%29
It becomes 1%2Ahighlight_green%28+a%5E%28-2-3%29+%29%2Ab%5E2%2F18%2Fb.
Look at 1%2Aa%5E%28-2-3%29%2Ahighlight_red%28+b%5E2+%29%2F18%2Fhighlight_red%28+b+%29.
Reduce similar several occurrences of highlight_red%28+b%5E2+%29 to highlight_green%28+b%5E%28-1%2B2%29+%29
It becomes 1%2Aa%5E%28-2-3%29%2Ahighlight_green%28+b%5E%28-1%2B2%29+%29%2F18.
Look at 1%2Aa%5E%28-2-3%29%2Ab%5E%28highlight_red%28+-1+%29%2B2%29%2F18.
Removed extra sign in front of -1
It becomes 1%2Aa%5E%28-2-3%29%2Ab%5E%28-highlight_green%28+1+%29%2B2%29%2F18.
Look at highlight_red%28+1+%29%2Aa%5E%28-2-3%29%2Ab%5E%28-1%2B2%29%2F18.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes a%5E%28-2-3%29%2Ab%5E%28-1%2B2%29%2F18.
Look at a%5E%28-highlight_red%28+2+%29-highlight_red%28+3+%29%29%2Ab%5E%28-1%2B2%29%2F18.
Added fractions or integers together
It becomes a%5E%28highlight_green%28+-5+%29%29%2Ab%5E%28-1%2B2%29%2F18.
Look at a%5E%28-5%29%2Ab%5E%28-highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%29%2F18.
Added fractions or integers together
It becomes a%5E%28-5%29%2Ab%5E%28highlight_green%28+1+%29%29%2F18.
Look at a%5E%28-5%29%2Ab%5Ehighlight_red%28+%281%29+%29%2F18.
Removing power of one highlight_red%28+%281%29+%29
Look at a%5E%28highlight_red%28+-5+%29%29%2Ab%2F18.
Removed extra sign in front of -5
It becomes a%5E%28-highlight_green%28+5+%29%29%2Ab%2F18.
Look at highlight_red%28+a%5E%28-5%29+%29%2Ab%2F18.
Negative power changes multiplication to division
It becomes 1%2Fhighlight_green%28+a%5E5+%29%2Ab%2F18.
Look at highlight_red%28+1+%29%2Fa%5E5%2Ab%2F18.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes b%2Fa%5E5%2F18.
Result: b%2Fa%5E5%2F18

Universal Simplifier and Solver

Welcome to Graphical Universal Mathematical Expression Simplifier and Algebra Solver (GUMESS).
It solves most middle school algebra equations and simplifies expressions, and it SHOWS ALL WORK. It is free to use.

Enter expression to be simplified, or equation to be solved.
I will figure out if what you typed is an equation.

Enter Expression ==>     
Examples: x^2-2x=-1, 3x-x-x+a-a=5, (x^2-1)/(x+1), 2x-(x+x)


Single letter variables only, no functions, xy means x*y, x(x-1) means x*(x-1), sin(x) means s*i*n*(x)


You must use the "*" (star) symbol for all multiplications! x(x+1) is WRONG! It means a function x of x-1. x*(x-1) is right. Use the ^ (caret) for exponentiation. x^2 means x squared. x/2y means x%2F2y
Resources: Simplifier Portal, help with entering simplifier formulas (a must read).


Or, click on any of these examples: 1, 2-1, 2%5E2-4%5E1, %281%29, -%28-1%29, %28%28%28%28x%29%29%29%29-x, -%28-%28-%28-%28-%28x%29%29%29%29%29%2Bx, %28%28%28%28x%29%29%29%29-y%2Ax%2A2%2Fy, %28x%2B1%29%2F%28x%2B1%29, %281%2Bx%29%2F%28x%2B1%29, %281%2Bx%29%2F%282%2A%28x%2B1%29%29, x-x%2Bx, x%2A%28y%2Az%29+-+%28x%2Ay%29%2Az, %28x-1%29%2A%28y-1%29-%28y-1%29%2A%28x-1%29, %28x-1%29%2A%28y-1%29-%28%28y-1%29%2Fx%29%5E%282-1%29%2A%28x-1%29%2Ax, 2%2A2%2A2%5E2%2Ax-x, 1%2F%282%2Bx%2Ay-y%2Ax%5E2%2F%28x%2B0%29%29, x%5E%28y%2Bz%29-x%5E%28z%2By%29, x-x%2F2, x=x, x%2B1=2, 0=5-x-7, %28x%5E2-x-2%29%2F%28%28x%2B1%29%2F%282x%2B2%29%29=0, %28x-1%29%28x-2%29%2F%28x%2B1%29=0, %28x%5E2-x-2%29=0, %28x%5E2-x-2%29%2A%28x%5E2-x-2%29%2F%28x%5E2%2B2%2Ax%2B1%29%2F%28x%5E2-4%2Ax%2B4%29, %28x%5E3-x%29%2Fx=0, %28x-1%29%2Fx=0, %282x%5E4-2%29%2F%28x-1%29=0, x%5E5-x%5E3=0, %28x-3%29%2A%28x%5E6-2x%5E3%2B1%29=0, , x%2A%28x-1%29%28x%2B1%29%2A%28x%5E3%2Bx%29, %28x-1%29%28x%2B1%29-3=0, %28x%5E2-1%29%28x%5E2%2B1%29-15=0, 1%2Fx%5E-1, x%2Fa%5E%28-5%29, x%2Aa%5E%28-5%29, x%5E-1, 2%2F6, 1%2F2-2%2F3, 1%2F2-1, 1%2F2-1%2B1%2F10, 1%2F2%2B2%2F3, 1%2F3%2B0.51, 1%2F3%2B0.5, x-x%2F3, 0.5x-x%2F3, 0.5x-2%2Ax%2F3, 1%2F2%2B1%2F3%2B1%2F6, %282x%2B2y%29%2F2, %28%28-4%2B10%29-%28-2%2B14%29%29%2F2%2A%282%29.
Please write to Igor Chudov, ichudov @ algebra.com, with questions or suggestions.

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This simplifier has been used 37263595 times.