5.
a)
[tex]a = 4^{\frac{7}{5}} = \sqrt[5]{4^{7}}\\\\b = \frac{4}{\sqrt[5]{16}} = \frac{4}{\sqrt[5]{4^{2}}}\\\\\\P = a\cdot b\\\\P =\sqrt[5]{4^{7}}\cdot\frac{4}{\sqrt[5]{4^{2}}}=4\cdot\sqrt[5]{\frac{4^{7}}{4^{2}}} = 4\cdot\sqrt{4^{5}} = 4\cdot 4 = \boxed{16}[/tex]
b)
[tex]a = 3^{-\frac{1}{4}}\\\\b = \sqrt[3]{3}\\\\c = \frac{1}{3^{-\frac{5}{4}}}\\\\\\V = a\cdot b\cdot c\\\\V = 3^{-\frac{1}{4}}\cdot\sqrt[3]{3}\cdot\frac{1}{3^{-\frac{5}{4}}} =\frac{3^{-\frac{1}{4}}}{3^{-\frac{5}{4}}}\cdot\sqrt[3]{3} = 3^{-\frac{1}{4}-(-\frac{5}{4})}\cdot\sqrt[3]{3} =3^{\frac{4}{4}}\cdot\sqrt[3]{3} = 3\cdot\sqrt[3]{3} =\boxed{ 3\sqrt[3]{3}}[/tex]
