Question 186777
{{{sqrt(a^2)/sqrt(b^5)}}} Start with the given expression.



{{{sqrt(a^2)/sqrt(b^2*b^2*b)}}} Factor {{{b^5}}} to get {{{b^2*b^2*b}}}



{{{sqrt(a^2)/(sqrt(b^2)*sqrt(b^2)*sqrt(b))}}} Break up the square root.



{{{a/(b*b*sqrt(b))}}} Take the square root of {{{a^2}}} to get 'a'. Take the square root of {{{b^2}}} to get 'b'



{{{a/(b^2*sqrt(b))}}} Multiply



{{{(a*sqrt(b))/(b^2*sqrt(b)*sqrt(b))}}} Multiply BOTH the numerator and denominator by {{{sqrt(b)}}}



{{{(a*sqrt(b))/(b^2*b)}}} Multiply {{{sqrt(b)}}} by itself to get 'b'



{{{(a*sqrt(b))/(b^3)}}} Multiply




So {{{sqrt(a^2)/sqrt(b^5)=(a*sqrt(b))/(b^3)}}} where both 'a' and 'b' are positive.