5.
[tex]a) \ (\frac{1}{4})^{4}\cdot20^{4} =(\frac{1}{4}\cdot20)^{4} = 5^{4} = 625[/tex]
[tex]b) \ 15^{3}\cdot(\frac{1}{5})^{3} = (15\cdot\frac{1}{5})^{3} =3^{3} = 27\\\\c) \ 24^{2}\cdot(\frac{1}{4})^{2} = (24\cdot\frac{1}{4})^{2} = 6^{2} = 36\\\\d) \ (\frac{1}{3})^{4}\cdot6^{4} = (\frac{1}{3}\cdot6)^{4} = 2^{4} = 16\\\\e) \ (\frac{8}{5})^{3}\cdot(\frac{5}{4})^{3} = (\frac{8}{5}\cdot\frac{5}{4})^{3} = 2^{3} = 8\\\\f) \ (\frac{36}{7})^{2}\cdot(\frac{7}{9})^{2} = (\frac{36}{7}\cdot\frac{7}{9})^{2} = 4^{2} = 16[/tex]
[tex]g) \ \frac{35^{2}}{7^{2}} = (\frac{35}{7})^{2} = 5^{2} = 25\\\\h) \ \frac{63^{2}}{9^{2}} = (\frac{63}{9})^{2} = 7^{2} = 49\\\\i) \ \frac{32^{3}}{16^{3}} = (\frac{32}{16})^{3} = 2^{3} = 8\\\\j) \ \frac{6^{3}}{18^{3}} = (\frac{6}{18})^{3} = (\frac{1}{3})^{3} = \frac{1}{27}[/tex]
[tex]k) \ 42^{2}:6^{2} = (42:6)^{2} = 7^{2} = 49\\\\l) \ 5^{4}:15^{4} = (5:15)^{4} = (\frac{1}{3})^{4} = \frac{1}{81}[/tex]
