[tex]a) \ \frac{(2^{19}\cdot2^{21})^{3}}{2^{118}} = \frac{(2^{19+21})^{3}}{2^{118}}=\frac{(2^{40})^{3}}{2^{118}} = \frac{2^{40\cdot3}}{2^{118}} = \frac{2^{120}}{2^{118}} = 2^{120-118} = 2^{2} = 4\\\\b) \ \frac{15^{30}\cdot32^{6}}{81^{7}\cdot10^{30}} = \frac{(3\cdot5)^{30}\cdot(2^{5})^{6}}{(3^{4})^{7}\cdot(5\cdot2)^{30}} = \frac{3^{30}\cdot5^{30}\cdot2^{30}}{3^{28}\cdot5^{30}\cdot2^{30}}=\frac{3^{30}}{3^{28}} =3^{2} = 9[/tex]
Wyjaśnienie
[tex]a^{m}\cdot a^{n} =a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\(a^{m})^{n} = a^{m\cdot n}[/tex]
