Oblicz:
a) (1 3/4)^6 * (2/7)^6 = ?
b) (4/5)^4 : (2 2/3)^4 = ?
c) (4 1/2)^3 * (-2/3)^3 * (-2)^3 = ?

[tex]a)\ \ (1\frac{3}{4})^6\cdot(\frac{2}{7})^6=(1\frac{3}{4}\cdot\frac{2}{7})^6=(\frac{\not7^1}{\not4_{2}}\cdot\frac{\not2^1}{\not7_{1}})^6=(\frac{1}{2})^6=\frac{1}{64}\\\\\\b)\ \ (\frac{4}{5})^4:(2\frac{2}{3})^4=(\frac{4}{5}:2\frac{2}{3})^4=(\frac{4}{5}:\frac{8}{3})^4=(\frac{\not4^1}{5}\cdot\frac{3}{\not8_{2}})^4=(\frac{3}{10})^4=\frac{81}{10000}[/tex]

[tex]c)\ \ (4\frac{1}{2})^3\cdot(-\frac{2}{3})^3\cdot(-2)^3=(4\frac{1}{2}\cdot\frac{2}{3}\cdot2)^3=(\frac{\not9^3}{\not2_{1}}\cdot\frac{\not4^2}{\not3_{1}})^3=(3\cdot2)^3=6^3=216[/tex]

Jola6609viz Jola6609viz · Answer 2

[tex]Zadanie\\\\a^n\cdot b^n=(a\cdot b)^n\\\\\frac{a^n}{b^n}=(\frac{a}{b})^n\\\\a)\\\\(1\frac{3}{4})^6\cdot(\frac{2}{7})^6= (\frac{7}{4}\cdot\frac{2}{7})^6=(\frac{1}{2})^6= \frac{1}{64}\\\\b)\\\\(\frac{4}{5})^4:(2\frac{2}{3})^4=(\frac{4}{5}:\frac{8}{3})^4= (\frac{4}{5} \cdot\frac{3}{8})^4=(\frac{3}{10})^4=\frac{81}{10000}=0,0081\\\\c)\\\\ (4\frac{1}{2})^3\cdot(-\frac{2}{3})^3\cdot(-2)^3=[\frac{9}{2}\cdot(-\frac{2}{3})\cdot (-2)]^3=(\frac{9}{2}\cdot\frac{4}{3})^3=6^3=216[/tex]