b) b=16\sqrt[3]2
log_216\sqrt[3]{2} = log_22^{\frac{13}{3}} = \frac{13}{3}
b=2^4*2^{\frac{1}{3}}=2^{\frac{12}{3}+\frac{1}{3}}=2^{\frac{13}{3}}
c)
b=\frac{\sqrt2}{8}
log_2\frac{\sqrt2}{8}=log_22^{-\frac{5}{2}}=-\frac{5}{2}
b=\frac{\sqrt2}{8}=\frac{2^{\frac{1}{2}}}{2^3}=2^{\frac{1}{2}-\frac{6}{2}}=2^{-\frac{5}{2}}
d)
b=\frac{\sqrt[3]{2}}{32}
log_2\frac{\sqrt[3]2}{32}=log_22^{-\frac{8}{3}}=-\frac{8}{3}
b=\frac{\sqrt[3]{2}}{32}=\frac{2^{\frac{1}{3}}}{2^5}=2^{\frac{5}{15}-\frac{45}{15}}=2^{-\frac{40}{15}} = 2^{-\frac{8}{3}}