Question

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Answer 1

Respuesta:

${ (- 4)}^{ - 5} \times {( - 4)}^{8} \times {( - 4)}^{ - 6} = {( - 4)}^{ - 5 + 8 - 6} = {( - 4)}^{ 8 - 11} = {( - 4)}^{ - 3} = \frac{1}{ {( - 4)}^{3} } \\ {(x)}^{ - 8} \times {(x)}^{10} \times {(x)}^{2} = {(x)}^{ - 8 + 10 + 2} = {(x)}^{ - 8 + 12} = {(x)}^{4} \\ {(23)}^{8} \times {(23)}^{ - 12} \times {(23)}^{2} = {(23)}^{ 8- 12 + 2} = {(23)}^{10 - 12} = {(23)}^{ - 2} = \frac{1}{ {(23)}^{2} } \\ ( {(6)}^{ \frac{2}{5} } \times {(6)}^{ \frac{3}{10} } ) \div ({{(6)}^{ \frac{1}{2} } })^{2} = {(6)}^{ \frac{2}{5} + \frac{3}{10} } \div {(6)}^{ \frac{1}{2} \times 2 } = {(6)}^{ \frac{7}{10} } \div {(6)}^{1} = {(6)}^{ \frac{7}{10} - 1 } = {(6)}^{ - \frac{ 3}{10} } = \frac{1}{ {(6)}^{ \frac{3}{10} } } \\ ({(t)}^{ \frac{3}{5} } \div {(t)}^{ \frac{3}{10} } ) \div ( { {t}^{ - \frac{1}{2} } })^{ \frac{6}{5} } = {(t)}^{ \frac{3}{5} - \frac{3}{10} } \div {(t)}^{ - \frac{1}{2} \times \frac{6}{5} } = {(t)}^{ \frac{3}{10} } \div {(t)}^{ - \frac{6}{10} } = {(t)}^{ \frac{3}{10} - ( - \frac{6}{10} ) } = {(t)}^{ \frac{3}{10} + \frac{6}{10} } = {(t)}^{ \frac{9}{10} } \\ {(27)}^{ - 2} \times ( \frac{1}{9} )^{ - 3} \times \sqrt[3]{ {(3)}^{4} } =( { {(3)}^{3} })^{ - 2} \times ({ {(3)}^{ - 2} })^{ - 3} \times {(3)}^{ \frac{4}{3} } = {(3)}^{2 \times ( - 3)} \times {(3)}^{( - 2) \times ( - 3)} \times {(3}^{ \frac{4}{3} } = {(3)}^{ - 6} \times {(3)}^{6} \times {(3)}^{ \frac{4}{3} } = {(3)}^{ - 6 + 6 + \frac{4}{3} } = {(3)}^{ \frac{4}{3} } \\ ( { \frac{1}{16} })^{5} \times \sqrt[5]{ {(4)}^{2} } \times {(64)}^{ - 1} = ({ {(4)}^{ - 2} })^{5} \times {(4)}^{ \frac{2}{5} } \times ({ {(4)}^{ 3} })^{ - 1} = {(4)}^{ - 2 \times 5} \times {(4)}^{ \frac{2}{5} } \times {(4)}^{3 \times ( - 1)} = {(4)}^{ - 10} \times {(4)}^{ \frac{2}{5} } \times {(4)}^{ - 3} = {(4)}^{ - 10 + \frac{2}{5} - 3 } = {(4)}^{ - 13 + \frac{2}{5} } = {(4)}^{ - \frac{63}{5} } = \frac{1}{ {(4)}^{ \frac{63}{5} } } \\ {(8)}^{4} \times {( \frac{1}{2}) }^{ - 3} \times \sqrt[3]{ {(2)}^{5} } = ({ {(2)}^{3} })^{4} \times( { {(2)}^{ - 1} })^{ - 3} \times {(2)}^{ \frac{5}{3} } = {(2)}^{3 \times 4} \times {(2)}^{( -1 ) \times ( - 3)} \times {(2)}^{ \frac{5}{3} } = {(2)}^{12} \times {(2)}^{3} \times {(2)}^{ \frac{5}{3} } = {(2)}^{12 + 3 + \frac{5}{3} } = {(2)}^{ \frac{50}{ 3} } \\ {(36)}^{4} \times {( \frac{1}{6}) }^{5} \times \sqrt[3]{ {(6)}^{4} } = ( { {(6)}^{2} })^{4} \times ( { {(6)}^{ - 1} )}^{5} \times {(6)}^{ \frac{4}{3} } = {(6)}^{2 \times 4} \times {(6)}^{ - 1 \times 5} \times {(6)}^{ \frac{4}{3} } = {(6)}^{8} \times {(6)}^{ - 5} \times {(6)}^{ \frac{4}{3} } = {(6)}^{8 - 5 + \frac{4}{3} } = {(6)}^{ \frac{13}{4} }$