Answer
$x^2y^3a^5b\sqrt { b}$.
Work Step by Step
The given expression is
$=\frac{6\sqrt {49xy}\sqrt {ab^2}}{7\sqrt {36x^{-3}y^{-5}}\sqrt{a^{-9}b^{-1}}}$
Multiply the radicands and retain the common index.
$=\frac{6\sqrt {49xy\cdot ab^2}}{7\sqrt {36x^{-3}y^{-5}\cdot a^{-9}b^{-1}}}$
Simplify.
$=\frac{6\sqrt {7^2xy\cdot ab^2}}{7\sqrt {6^2x^{-3}y^{-5}\cdot a^{-9}b^{-1}}}$
$=\frac{6\cdot 7 \sqrt {xy\cdot ab^2}}{7\cdot 6 \sqrt {x^{-3}y^{-5}\cdot a^{-9}b^{-1}}}$
Cancel common terms.
$=\frac{ \sqrt {xy\cdot ab^2}}{ \sqrt {x^{-3}y^{-5}\cdot a^{-9}b^{-1}}}$
Divide the radicands and retain the common index.
$=\sqrt {\frac{ xy\cdot ab^2}{x^{-3}y^{-5}\cdot a^{-9}b^{-1}}}$
Divide factors in the radicand. Subtract exponents on common bases.
$=\sqrt { x^{1+3}y^{1+5}a^{1+9}b^{2+1}}$
Simplify.
$=\sqrt { x^{4}y^{6}a^{10}b^{3}}$
$=x^2y^3a^5b\sqrt { b}$.
