Answer
$s^{\frac{5}{4}}$
Work Step by Step
RECALL:
(i) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$
(ii) $(a^m)^n=a^{mn}$
(iii) $a^m \cdot a^n = a^{m+n}$
Use rule (i) above to obtain:
$=\sqrt{s\cdot s^{\frac{3}{2}}}$
Use rule {iii) to obtain:
$=\sqrt{s^{1+\frac{3}{2}}}
\\=\sqrt{s^{\frac{2}{2}+\frac{3}{2}}}
\\=\sqrt{s^{\frac{5}{2}}}$
Use rule (i) to obtain:
$=(s^{\frac{5}{2}})^{\frac{1}{2}}$
Use rule (ii) above to obtain:
$=s^{\frac{5}{2}\cdot \frac{1}{2}}
\\=s^{\frac{5}{4}}$
