zad. 1
[tex]a) \: {a}^{7} \div {a}^{5} = {a}^{7 - 5} = {a}^{2} [/tex]
[tex]b) \: {( {b}^{4}) }^{7} = {b}^{4 \times 7} = {b}^{28} [/tex]
[tex]c) \: \frac{ {c}^{9} }{c} = {c}^{9 - 1} = {c}^{8} [/tex]
[tex]d) \: d \times {d}^{5} = {d}^{1 + 5} = { {d}^{6} \: }[/tex]
[tex]e) \: \frac{ {x}^{6} }{ {y}^{6} } = {( \frac{x}{y}) }^{6} [/tex]
[tex]f) \: {m}^{10} \times {n}^{10} = {(mn})^{10} [/tex]
zad. 2
[tex]a) \: {9}^{5} =( ({3})^{2} )^{5} = {3}^{10} [/tex]
[tex]b) \: {15}^{9} \div {5}^{9} = (15 \div 5) ^{9} = {3}^{9} [/tex]
[tex]c) \: {6}^{7} \times {0.5}^{7} = (6 \times 0.5) ^{7} = {3}^{7} [/tex]
[tex]d) \: \frac{ {3}^{8} }{81} = \frac{ {3}^{8} }{ {3}^{4} } = {3}^{4} [/tex]
[tex]e) \: 27 \times {3}^{7} = {3}^{3} \times {3}^{7} = {3}^{10} [/tex]
[tex]f) \: {9}^{6} \div {3}^{5} = ( {3}^{2} )^{6} \div {3}^{5} = {3}^{7} [/tex]
zad. 3
[tex]a) \: ( \frac{1}{3} ) ^{5} \times {6}^{5} = ( \frac{1}{3} \times 6) ^{5} = {2}^{5} = 32[/tex]
[tex]b) \: ( \frac{1}{5} ) ^{7} \times 5^{4} = {5}^{ - 7} \times {5}^{4} = {5}^{ - 3} = ( \frac{1}{5} )^{3} = \frac{1}{125} [/tex]
[tex]c) \: \frac{ {6}^{7} }{ {6}^{5} } = {6}^{2} = 36[/tex]
[tex]d) \: {21}^{3} \div {7}^{3} = (21 \div 7) ^{3} = {3}^{3} = 27[/tex]
[tex]e) \: (( \frac{1}{2} )^{4} )^{2} \times {2}^{8} = ( \frac{1}{2} ) ^{8} \times {2}^{8} = ( \frac{1}{2} \times 2)^{8} = 1[/tex]
