oblicz wartość wyrażenia a)[latex] (frac{2}{3})^{5}*(frac{3}{4})^{5} [/latex] b)[latex] (frac{1}{2})^{4}*(frac{2}{3})^{4} [/latex] c)[latex] (1frac{1}{2})^{50}*(frac{2}{3})^{50} [/latex] d)[latex] (2frac{1}{3})^{4}*(frac{6}{7})^{4} [/latex]

[latex]a) \ (frac{2}{3})^5 cdot (frac{3}{4})^5=(frac{2}{3} cdot frac{3}{4})^5=(frac{1}{2})^5=frac{1}{32} \ b) \ (frac{1}{2})^4 cdot (frac{2}{3})^4=(frac{1}{2} cdot frac{2}{3})^4=(frac{1}{3})^4=frac{1}{81}\ c) \ (1frac{1}{2})^{50} cdot (frac{2}{3})^{50}=(frac{3}{2} cdot frac{2}{3})^{50}=1^{50}=1 \ d) \ (2frac{1}{3})^4 cdot (frac{6}{7})^4=(frac{7}{3} cdot frac{6}{7})^4=2^4=16[/latex]

[latex]a) ( frac{2}{3})^5 cdot ( frac{3}{4} )^5= (frac{2}{3} cdot frac{3}{4})^5=(frac{6}{12})^5= (frac{1}{2})^5= frac{1}{32}\ \ b) ( frac{1}{2})^4 cdot ( frac{2}{3} )^4=( frac{1}{2} cdotfrac{2}{3} )^5=( frac{2}{6} )^4=( frac{1}{3} )^4= frac{1}{81}\ \ c) (1frac{1}{2})^{50} cdot (frac{2}{3})^{50}=(1frac{1}{2}cdotfrac{2}{3})^{50}=(frac{3}{2}cdotfrac{2}{3})^{50}=(frac{6}{6})^{50}=1^{50}=1[/latex] [latex]d) (2frac{1}{3})^4cdot(frac{6}{7})^4=(2frac{1}{3}cdotfrac{6}{7})^4=(frac{7}{3}cdotfrac{6}{7})^4=(frac{42}{21})^4=2^4=16[/latex]