To simplify: The expression and eliminate coefficients if any: a) sqrt[4]{b^{3}} sqrt{b} b) (2sqrt{a}) (sqrt[3]{a^{2}})

a) Definition used:
Definition of rational exponents:
"For any rational exponent ${\displaystyle \frac{m}{n}}$ in its lowest terms, where m and n are integers and ${\displaystyle n>0}$ we define, ${\displaystyle {\left(a\right)}^{\frac{m}{n}}=\sqrt{n}\left\{{\left(a\right)}^m\right\}={\left(\sqrt{n}\left\{a\right\}\right)}^m}$
Formula used:
"The product of two powers with the same base a and different exponents m and n is given by, ${\displaystyle a^m\times a^n=a^{m+n}}$
That is, while multiplying two powers with same base, the exponents are added and the base will remain the same.
Calculation:
The given expression is ${\displaystyle \sqrt{4}\left\{b^3\right\}\sqrt{b}.}$
Use the definition of rational exponents and the above formula and simplify the expression as shown below.
${\displaystyle \sqrt{4}\left\{b^3\right\}\sqrt{b}=b^{\frac{3}{4}}\cdot b^{\frac{1}{2}}}$
${\displaystyle =b^{\frac{3}{4}+\frac{1}{2}}}$
${\displaystyle =b^{\frac{5}{4}}}$
Therefore, the simplified form of the expression is ${\displaystyle b^{\frac{5}{4}}}$
b) Use the definition of rational exponents and the formula mentioned in sub part (a) and simplify the expression as shown below.
${\displaystyle \left(2\sqrt{a}\right)\left(\sqrt{3}\left\{a^2\right\}\right)=\left(2a^{\frac{1}{2}}\right)\left(a^{\frac{2}{3}}\right)}$
${\displaystyle =2a^{\frac{1}{2}+\frac{2}{3}}}$
${\displaystyle =2a^{\frac{7}{6}}}$
Therefore, the simplified form of the expression is ${\displaystyle 2a^{\frac{7}{6}}}$