Evaluate
\frac{\sqrt{5}\left(\sqrt{5}x^{\frac{3}{2}}-1\right)^{15}}{390625x^{\frac{15}{2}}}
Expand
x^{15}-3\sqrt{5}x^{\frac{27}{2}}+21x^{12}-\frac{91\sqrt{5}x^{\frac{21}{2}}}{5}+\frac{273x^{9}}{5}-\frac{3003\sqrt{5}x^{\frac{15}{2}}}{125}+\frac{1001x^{6}}{25}-\frac{1287\sqrt{5}x^{\frac{9}{2}}}{125}+\frac{1287x^{3}}{125}-\frac{1001\sqrt{5}x^{\frac{3}{2}}}{625}+\frac{3003}{3125}-\frac{273\sqrt{5}}{3125x^{\frac{3}{2}}}+\frac{91}{3125x^{3}}-\frac{21\sqrt{5}}{15625x^{\frac{9}{2}}}+\frac{3}{15625x^{6}}-\frac{\sqrt{5}}{390625x^{\frac{15}{2}}}
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