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[tex]1) {4}^{ - 1} = \frac{1}{4} = 0.25 \\ 2) {(0.1)}^{ - 2} = {( \frac{1}{10}) }^{ - 2} = {10}^{2} = 100 \\ 3) {( \frac{2}{3} )}^{ - 4} = {( \frac{3}{2} )}^{4} = \frac{81}{16} = 5 \frac{1}{16} = 5 \frac{625}{10000} = 5.0625 \\ 4) { - 10}^{ - 3} = - \frac{1}{ {10}^{3} } = - \frac{1}{1000} = - 0.001 \\ 5) {( - 0.7)}^{0} = 1[/tex]

[tex]1) {x}^{ - 6} \times {x}^{4} = {x}^{ - 2} = \frac{1}{ {x}^{2} } \\ 2) {x}^{4} \div {x}^{ - 5} = {x}^{4 - ( - 5)} = {x}^{9} \\ 3) \frac{ {x}^{5} \times {x}^{ - 7} }{ {x}^{ - 4} } = \frac{ {x}^{ - 2} }{ {x}^{ - 4} } = \frac{ {x}^{4} }{ {x}^{2} } = {x}^{2} [/tex]

[tex]1) {( \frac{2x + 1}{x}) }^{ - 3} \times ( {x}^{ - 2} + 4 {x}^{ - 1} + 4) = \frac{ {x}^{3} }{ {(2x + 1)}^{3} } \times ( \frac{1}{ {x}^{2} } + \frac{4}{x} + 4) = \frac{ {x}^{3} }{ {(2x + 1)}^{3} } \times \frac{1 + 4x + 4 {x}^{2} }{ {x}^{2} } = \frac{ {(2x + 1)}^{2} }{ {(2x + 1)}^{3} } = \frac{1}{2x + 1 } \\ 2)( \frac{1}{a} - \frac{1}{2b} ) \times {( \frac{a - 2b}{ {a}^{2} {b}^{2} } )}^{ - 1} = \frac{2b - a}{2ab} \times \frac{ {a}^{2} {b}^{2} }{a - 2b} = \frac{(2b - a) \times ab \times ab}{2ab \times ( - 1)( 2b - a)} = \frac{ab}{ - 2} = - \frac{ab}{2} [/tex]