Answer
$b^2\sqrt[4]{b}$
Work Step by Step
RECALL:
(i) $a^m \cdot a^n = a^{m+n}$
(ii) $\sqrt[n]{a} = a^{\frac{1}{n}}$
(iii) $a^{\frac{m}{n}}=\sqrt[n]{a^m}$
Use rule (iii) to have:
$=b^{\frac{3}{2}}\cdot b^{\frac{3}{4}}
\\=b^{\frac{6}{4} + \frac{3}{4}}
\\=b^{\frac{9}{4}}$
Use rule (i) to have:
$\\=a^{\frac{1}{2} + \frac{1}{3}}
\\=a^{\frac{3}{6} + \frac{2}{6}}
\\=a^{\frac{5}{6}}$
Use rule (iii) to have:
$=\sqrt[4]{b^9}
\\=\sqrt[4]{b^8(b)}
\\=b^2\sqrt[4]{b}$
