Answer
$b^{\frac{11}{9}} c^{\frac{5}{4}}$.
Work Step by Step
The given expression is
$=(b^{\frac{2}{3}}\cdot c^{\frac{3}{4}})(b^{\frac{5}{9}}\cdot c^{\frac{1}{2}})$
Clear the parentheses.
$=b^{\frac{2}{3}}\cdot b^{\frac{5}{9}}\cdot c^{\frac{3}{4}}\cdot c^{\frac{1}{2}}$
Use power law:
$=b^{\left (\frac{2}{3}+\frac{5}{9}\right )}\cdot c^{\left (\frac{3}{4}+\frac{1}{2}\right )}$
$=b^{\frac{6+5}{9}}\cdot c^{\frac{3+2}{4}}$
Simplify.
$=b^{\frac{11}{9}} c^{\frac{5}{4}}$.
