Odpowiedź:
a)
[tex]( - \frac{1}{2} {)}^{3} \cdot \: ( -\frac{1}{2} {)}^{4} \cdot \: 2^7=( - 1 {)}^{7} \cdot \: ( \frac{1}{2} {)}^{3} \cdot ( - 1 {)}^{4} \cdot \: ( \frac{1}{2} {)}^{4} \cdot \: ( (\frac{1}{2} {)}^{ - 1} )^7= - 1 \cdot \: (\frac{1}{2} {)}^{3 + 4 - 7} = - 1 \cdot \: (\frac{1}{2} {)}^{0} = - 1[/tex]
b)
[tex] {0.1}^{8} \cdot \: {0.2}^{8} \div {0.02}^{6} = (0.1 \cdot \: 0.2 {)}^{8} \div 0.0 {2}^{6} = 0.02 ^{8} \div 0.0 {2}^{6} = 0.02 ^{8 - 6} = {0.02}^{2} [/tex]
c)
[tex]0. {5}^{6} \cdot \: ( - 0.5 {)}^{7} \div 0.05 ^{13} = {0.5}^{6} \cdot \: ( - 1 {)}^{7} \cdot \: 0. {5}^{7} \div 0.0 {5}^{13} = - 1 \cdot \: {0.5}^{6 + 7} \div 0.0 {5}^{13} = - ({0.5})^{13} \div {0.05}^{13} = - (0.5 \div 0.05 {)}^{13} = - {10}^{13} [/tex]
d)
[tex] \frac{ {44}^{4} }{ {22}^{3} } = \frac{ {2}^{4} \cdot \: {22}^{4} }{ {22}^{3} } = {2}^{4} \cdot \: 22 = {2}^{4} \cdot \: 2 \cdot \: 11 = {2}^{5} \cdot \: 11[/tex]
e)
[tex] \frac{ {64}^{2} \cdot \: {36}^{2} }{ {6}^{3} \cdot \: {2}^{7} } = \frac{( {2}^{6} {)} ^{2} \cdot \: ( {6}^{2} )^{2} }{ {6}^{3} \cdot \: {2}^{7} } = \frac{ {2}^{12} \cdot \: {6}^{4} }{ {6}^{3} \cdot \: {2}^{7} } = {2}^{5} \cdot \: 6 = {2}^{5} \cdot \: 2 \cdot \: 3 = {2}^{6} \cdot \: 3[/tex]
f)
[tex] \frac{ {4}^{6} \cdot \: {8}^{6} }{ {32}^{5} } = \frac{(4 \cdot \: 8 {)}^{6} }{ {32}^{5} } = \frac{ {32}^{6} }{ {32}^{5} } = 32 = {2}^{5} [/tex]
