1.
a
[tex] \frac{5^3*5^8}{5^{11}:5^2}= \frac{5^{3+8}}{5^{11-2}}= \frac{5^{11}}{5^9}=5^{11-9}=5^2=25 [/tex]
b
[tex] \frac{ (\frac{3}{7})^{10} *(\frac{14}{3})^{10} }{(2^3)^3} = \frac{( \frac{3}{7}* \frac{14}{3})^{10} }{2^{3*3}}= \frac{2^{10}}{2^9}=2 [/tex]
c
[tex] \frac{0,25^3:0,5^3}{5^3} = \frac{(0,25:0,5)^3}{5^3}= ( \frac{0,5}{5})^3=0,1^3=0,001 [/tex]
d
[tex]( \frac{1}{3})^{-1}* (\frac{1}{3})^{-2} =( \frac{1}{3})^{(-1)+(-2)}= (\frac{1}{3})^{-3}=3^3=27[/tex]
e
[tex]( \frac{2}{5})^{-3}: (-\frac{2}{5})^{-2}=( \frac{2}{5})^{(-3)-(-2)}= (\frac{2}{5})^{-1}= \frac{5}{2}=2 \frac{1}{2} [/tex]
f
[tex](0,2^{-1})^{-3}=0,2^{(-1)*(-3)}=0,2^3=0,008[/tex]
2.
a
[tex]3 \sqrt{6}+ \sqrt{ \frac{6}{4} }=3 \sqrt{6}+ \frac{ \sqrt{6} }{ \sqrt{4} }=3 \sqrt{6}+ \frac{1}{2}\sqrt{6}=3 \frac{1}{2} \sqrt{6}[/tex]
b
[tex](3 \sqrt{ \frac{5}{2} })^2=3^2*( \sqrt{ \frac{5}{2} })^2= 9*\frac{5}{2}= \frac{45}{2}= 22 \frac{1}{2} [/tex]
c
[tex](- \frac{1}{2} \sqrt{3})^3=(- \frac{1}{2})^3*( \sqrt{3})^3=- \frac{1}{8}*3 \sqrt{3} =- \frac{3}{8}\sqrt{3}[/tex]
d
[tex]( \sqrt{ \frac{2}{2} })^3= ( \sqrt{1})^3=1^3=1[/tex]
3.
a
[tex] \sqrt{5}* \sqrt{8}= \sqrt{5*8}= \sqrt{40}= \sqrt{4*10}= 2 \sqrt{10} [/tex]
b
[tex]3 \sqrt{2}*2 \sqrt{8}* \sqrt{3}= 3 \sqrt{2}*2 \sqrt{4*2}* \sqrt{3}= 3*2*2*( \sqrt{2} * \sqrt{2})* \sqrt{3}= \\ =12*2* \sqrt{3}=24 \sqrt{3} [/tex]
c
[tex]7 \sqrt{2}*0,1 \sqrt{12}=7*0,1* \sqrt{2*12}= 0,7 \sqrt{4*6}=0,7*2 \sqrt{6}=1,4 \sqrt{6}[/tex]
d
[tex] \sqrt[3]{16}+ \sqrt[3]{2} =\sqrt[3]{8*2}+ \sqrt[3]{2}=2\sqrt[3]{2}+ \sqrt[3]{2}=3\sqrt[3]{2}[/tex]
e
[tex]2 \sqrt[3]{24}-2 \sqrt[3]{3} =2 \sqrt[3]{8*3}-2 \sqrt[3]{3} =2*2 \sqrt[3]{3}-2 \sqrt[3]{3} =4\sqrt[3]{3}-2 \sqrt[3]{3} =2 \sqrt[3]{3} [/tex]
f
[tex]- \sqrt[3]{81} - \sqrt[3]{-3} =- \sqrt[3]{27*3} -(- \sqrt[3]{3}) =-3\sqrt[3]{3} + \sqrt[3]{3} =-2 \sqrt[3]{3} [/tex]
