Question 736563
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(y^2/3)^3/4 simplify
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<pre>
We are given this expression  (y^(2/3))^(3/4)  to simplify.


We can consider it as a formula to calculate a value, like a machinery, or as an algorithm, or as a function.


Then the domain of this function is the set of all real numbers, 
     including positive numbers, negative numbers and 0 (zero).



According to Algebra rules, we should multiply the indexes.


So, if 'y' is non-negative,  y >= 0,  then it is simplified to


    y^((2/3)*(3/4)) = y^(1/2) = {{{sqrt(y)}}}.


But if 'y' is negative,  then this formula is like a lame horse, because

the left side expression is defined at negative real values of 'y', while the right 

side,  {{{sqrt(y)}}},  is not defined at negative values of 'y'.


So, if we want formula  y^((2/3)*(3/4) = {{{sqrt(y)}}}  be valid for negative  'y',  too,
we should modify it this way 

    y^((2/3)*(3/4)) = {{{sqrt(abs(y))}}}.


Then both sides will be identical over the whole domain of all real numbers.
</pre>

Solved.