[tex]\displaystyle\bf\\f)\\\\\left(8\frac{1}{3}\right)^{\b4}\cdot\left(\frac{24}{10}\right)^{\b4}=\\\\\\=\left(\frac{8\cdot3+1}{3}\right)^{\b4}\cdot\left(\frac{24}{10}\right)^{\b4}=\\\\\\=\left(\frac{25}{3}\right)^{\b4}\cdot\left(\frac{24}{10}\right)^{\b4}=\\\\\\=\left(\frac{25}{3}\cdot\frac{24}{10}\right)^{\b4}=\\\\\\=\left(\frac{25\cdot24}{3\cdot10}\right)^{\b4}=\\\\\\=\left(\frac{5\cdot8}{1\cdot2}\right)^{\b4}=\\\\\\=\left(\frac{40}{2}\right)^{\b4}=\boxed{\bf20^{\b4}}=\boxed{\bf160000}[/tex]
