Question 75667
{{{((y^5)^3(y^3)^2)/(y^4)^4}}}
When you raise a base with an exponent to an exponent, you multiply the exponents:
in other words, 
{{{(x^y)^z=x^(y*z)}}} So in our problem {{{(y^5)^3=y^(3*5)=y^15}}} and we do this for every exponent raised to an exponent
{{{((y^(5*3))(y^(3*2)))/(y^(4*4))}}}
{{{((y^(15))(y^(6)))/(y^(16))}}}
Now when you are multiplying like bases with exponents, you add the exponents ie {{{x^2*x^3=x^(2+3)=x^5}}}. So it becomes:
{{{((y^(15+6)))/(y^(16))}}}
{{{((y^(21)))/(y^(16))}}}
When you divide like bases with exponents you subtract the exponents ie {{{x^3/x^2=x^(3-2)=x^1=x}}}
{{{y^(21-16)}}}
{{{y^(5)}}}
So the whole thing reduces down to {{{y^5}}} in other words
{{{((y^5)^3(y^3)^2)/(y^4)^4=y^5}}}