Answer
$a)$ $16b^{3/4}$
$b)$ $45a^{2}$
Work Step by Step
$a)$ $(4b)^{1/2}(8b^{1/4})$
Raise each factor inside the first parentheses to the power of $\dfrac{1}{2}$:
$(4b)^{1/2}(8b^{1/4})=(4^{1/2})(b^{1/2})(8b^{1/4})=...$
Knowing that $4^{1/2}=\sqrt{4}=2$, evaluate the products and simplify:
$...=(2)(b^{1/2})(8b^{1/4})=16b^{1/2+1/4}=16b^{3/4}$
$b)$ $(3a^{3/4})^{2}(5a^{1/2})$
Square each factor inside the first parentheses:
$(3a^{3/4})^{2}(5a^{1/2})=(3^{2})(a^{3/2})(5a^{1/2})=(9)(a^{3/2})(5a^{1/2})=...$
Evaluate the products and simplify:
$...=45a^{3/2+1/2}=45a^{4/2}=45a^{2}$
