Question 173280
{{{4/(root(3,5x^2))}}} Start with the given expression



{{{(4*root(3,5x^2)root(3,5x^2))/(root(3,5x^2)root(3,5x^2)root(3,5x^2))}}} Multiply the fraction by {{{root(3,5x^2)/root(3,5x^2)}}} twice (to get a total of 3 copies of {{{root(3,5x^2)}}} in the denominator)




Now notice how {{{root(3,5x^2)root(3,5x^2)root(3,5x^2)=root(3,(5x^2)(5x^2)(5x^2))=root(3,(5x^2)^3)=5x^2}}} 



So let's replace the denominator with {{{5x^2}}}



{{{(4*root(3,5x^2)root(3,5x^2))/(5x^2)}}} 



Now multiply {{{4*root(3,5x^2)root(3,5x^2)}}} out to get {{{4*root(3,5x^2)root(3,5x^2)=4*root(3,(5x^2)^2)=4*root(3,25x^4)=4x*root(3,25x)}}}




So replace the the numerator with


{{{(4x*root(3,25x))/(5x^2)}}} 



{{{(4*root(3,25x))/(5x)}}} Reduce {{{(4x)/(5x^2)}}} to get {{{4/(5x)}}}




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Answer:



So {{{4/(root(3,5x^2))}}} simplifies to {{{(4*root(3,25x))/(5x)}}}



In other words, {{{4/(root(3,5x^2))=(4*root(3,25x))/(5x)}}} where {{{x<>0}}}