zad. 1
[tex]a) {0}^{6} = 0 \\ b)(1 \frac{3}{7} {)}^{2} = ( \frac{10}{7} {)}^{2} = \frac{100}{49} \\c)( - 10 {)}^{0} = 1 \\ d) {2}^{5} = 32 \\ e) - 0. {3}^{2} = - 0.09 \\ [/tex]
[tex]f)( \frac{3}{4} {)}^{2} - \frac{ {3}^{2} }{4} + \frac{3}{ {4}^{2} } = \frac{9}{16} - \frac{9}{4} + \frac{3}{16} = \frac{9}{16} - \frac{36}{16} + \frac{3}{16} = - \frac{24}{16} = - \frac{3}{2} [/tex]
[tex]g) {4}^{6} = {2}^{a} \\ ( {2}^{2} {)}^{6} = {2}^{a} \\ {2}^{12} = {2}^{a} \\ a = 12[/tex]
[tex]h) {3}^{10} = {h}^{5} \\ ( {3}^{2} {)}^{5} = {h}^{5} \\ {9}^{5} = {h}^{5} \\ h = 9 \\ i) \frac{ {5}^{8} \times {2}^{9} }{ {10}^{7} } = \frac{ {5}^{8} \times {2}^{9} }{ {5}^{7} \times {2}^{7} } = {5}^{1} \times {2}^{2} = 5 \times 4 = 20[/tex]
[tex]j) {3}^{3} - {2}^{3} = 27 - 8 = 19[/tex]
zad. 2
[tex]a) \frac{ {a}^{9} \times {a}^{6} }{ {a}^{4} } = \frac{ {a}^{15} }{ {a}^{4} } = {a}^{11} \\ b)27 \times {3}^{5} \div 9 = {3}^{3} \times {3}^{5} \div {3}^{2} = {3}^{3 + 5 - 2} = {3}^{6} \\ c) {5}^{7} \div ( - 5 {)}^{4} = {5}^{7} \div {5}^{4} = {5}^{3} \\ d)( {6}^{5} {)}^{4} = {6}^{20} \\ e)( - 4 {}^{3} {)}^{2} {)}^{7} = ( - 4 {)}^{3 \times 2 \times 7} = ( - 4 {)}^{42} = {4}^{42} [/tex]
[tex]f)( \frac{3}{5} {)}^{3} \div ( \frac{1}{5} {)}^{3} = ( \frac{3}{5} \times 5 {)}^{3} = {3}^{3} \\ g)( \frac{1}{2} {)}^{4} \times {4}^{4} = 2 {}^{ - 4} \times ( {2}^{2} {)}^{4} = {2}^{ - 4} \times {2}^{8} = {2}^{4} \\ h) {8}^{4} \div {2}^{5} = ({2}^{3} {)}^{4} \div {2}^{5} = {2}^{12} \div {2}^{5} = {2}^{7} [/tex]
zad. 3
[tex] \frac{ {5}^{4} \times {5}^{2} }{( {5}^{2} {)}^{4} \div {5}^{3} } = \frac{ {5}^{6} }{ {5}^{8} \div {5}^{3} } = \frac{ {5}^{6} }{ {5}^{5} } = {5}^{1} = 5[/tex]
[tex] \frac{16 \times {3}^{5} \times {2}^{7} }{ {8}^{2} \times 27 \times {2}^{6} } = \frac{ {2}^{4} \times {3}^{5} \times {2}^{7} }{( {2}^{3} {)}^{2} \times {3}^{3} \times {2}^{2} } = \frac{ {2}^{11} \times {3}^{5} }{ {2}^{6} \times {3}^{3} \times {2}^{2} } = \frac{ {2}^{11} \times {3}^{5} }{ {2}^{8} \times {3}^{3} } = {2}^{3} \times {3}^{2} = 8 \times 9 = 72[/tex]
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