d)
\frac{16\sqrt[3]2*\sqrt8}{8^{\frac{2}{3}}*\sqrt[4]2}=\frac{8*2*2^{\frac{1}{3}}*8^{\frac{1}{2}}}{8^{\frac{2}{3}}*2^{\frac{1}{4}}}=
8^{\frac{3}{2}-\frac{2}{3}}*2^{\frac{4}{3}-\frac{1}{4}}=8^{\frac{9}{6}-\frac{4}{6}}*2^{\frac{16}{12}-\frac{3}{12}}=
8^{\frac{5}{6}}*2^{\frac{13}{12}}=(2^3)^{\frac{5}{6}}*2^{\frac{13}{12}}=
2^{\frac{30}{12}}*2^{\frac{13}{12}}=2^{\frac{43}{12}}=2^{\frac{36}{12}}*2^{\frac{7}{12}}=
2^3*2^{\frac{7}{12}}=8*2^{\frac{7}{12}}