Answer
$5$
Work Step by Step
RECALL:
(1) $a^m \cdot a^n = a^{m+n}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
Use rule (1) above to obtain:
$=\dfrac{5^{\frac{3}{4}+\frac{1}{2}}}{5^{\frac{1}{4}}}
\\=\dfrac{5^{\frac{3}{4}+\frac{2}{4}}}{5^{\frac{1}{4}}}
\\=\dfrac{5^{\frac{3+2}{4}}}{5^{\frac{1}{4}}}
\\=\dfrac{5^{\frac{5}{4}}}{5^{\frac{1}{4}}}$
Use rule (2) above to obtain:
$=5^{\frac{5}{4} - \frac{1}{4}}
\\=5^{\frac{5-1}{4}}
\\=5^{\frac{4}{4}}
\\=5^{1}
\\=5$
