Zadanie 1 strona 30 a) [latex](frac{2}{3})^3cdot(frac{2}{3})^2=(frac{2}{3})^{3+2}=(frac{2}{3})^5[/latex] b) [latex](3^3cdot2^3)^2=(3^3)^2cdot(2^3)^2=3^{3cdot2}cdot2^{3cdot2}=3^6cdot2^6=(3cdot2)^6=6^6[/latex] c) [latex](3^2)^4=3^{2*4}=3^8[/latex] d) [latex](frac{2}{7})^5cdot7^5=(frac{2}{7}cdot7)^5=2^5[/latex] e) [latex]1,5^8:1,5^3=1,5^{8-3}=1,5^5[/latex] f) [latex]2,5^{10}:25^{10}=(2,5:25)^{10}=0,1^{10}[/latex] ZADANIE 2 strona 30 a) [latex](3^2)^3:3^5=3^{2*3}:3^5=3^{6-5}=3^1=3[/latex] b) [latex](frac{5^4}{5^2})^2=(5^{4-2})^2=(5^2)^2=5^{2cdot2}=5^4=5cdot5cdot5cdot5=25*25=625[/latex] c) [latex](frac{2}{5})^7cdot2,5^6=frac{2^7}{5^7}cdot(frac{25:5}{10:5})^6=frac{2^7:2^6}{5^7:5^6}cdotfrac{5^6:5^6}{2^6:2^6}=frac{2^{7-6}}{5^{7-6}}cdotfrac{5^{6-6}}{2^{6-6}}=frac{2^1}{5^1}*frac{5^0}{2^0}=\\ =frac{2}{5}cdotfrac{1}{1}=frac{2}{5}[/latex] d) [latex]frac{4^5}{2^7}cdot5^3=frac{(2^2)^5}{2^7}cdot5^3=frac{2^{10}}{2^7}cdot5^3=2^{10-7}cdot5^3=2^3cdot5^3=(2cdot5)^3=\\=10^3=10cdot10cdot10=1000[/latex] e) [latex]frac{9^3cdot4^4}{6^{10}}=frac{3^6cdot2^6cdot2^2}{6^{10}}=frac{(3cdot2)^6cdot2^2}{6^{10}}=frac{6^6cdot2^2}{6^{6}cdot6^4}=frac{1cdot2^2}{1cdot6^4}=frac{2^2}{6^4}=frac{4:4}{1296:4}=frac{1}{324}[/latex] f) [latex]frac{0,25^3:0,5^3}{5^3}=frac{(0,25:0,5)^3}{5^3}=frac{0,5^3}{5^3}=(0,5:5)^3=0,1^3=0,001[/latex] Zadanie 9str 31 a) [latex]sqrt{2}cdotsqrt6=sqrt{12}=sqrt{2^2*3}=2sqrt3[/latex] b) [latex]2sqrt{3}cdotsqrt{18}=2sqrt{3cdot18}=2sqrt{54}=2sqrt{3^2cdot6}=2cdot3cdotsqrt6=6sqrt6[/latex] c) [latex]7sqrt{10}cdotfrac{1}{2}sqrt5=7cdotfrac{1}{2}cdotsqrt{10cdot5}=frac{7}{2}cdotsqrt{5^2cdot2}=frac{7cdot5}{2}sqrt2=frac{35}{2}sqrt2=17frac{1}{2}sqrt2[/latex] d) [latex]sqrt{50}+sqrt2=sqrt{5^2cdot2}+sqrt2=5sqrt2+sqrt2=6sqrt2 [/latex] e) [latex]sqrt{300}-2sqrt{3}=sqrt{10^2cdot3}-2sqrt3=10sqrt3-2sqrt3=8sqrt3[/latex] f) [latex]-2sqrt{32}-2sqrt{8}=-2sqrt{4^2cdot2}-2sqrt{2^2cdot2}=-2cdot4sqrt2-2cdot2sqrt2=\\=-8sqrt2-4sqrt2=-12sqrt2[/latex] pozdrawiam i licze na naj :)
