[tex]a) \: \sqrt{7} ^{ - 2} = (\frac{1}{ \sqrt{7} } ) ^{2} = (\frac{ \sqrt{7} }{7}) ^{2} = \frac{7}{49} = \frac{1}{7} [/tex]
[tex]b) \: ( - \sqrt{5} ) ^{ - 3} = ( - \frac{1}{ \sqrt{5} }) ^{3} = ( - \frac{ \sqrt{5} }{5} ) ^{3} = - \frac{ \sqrt{125} }{125} = - \frac{5 \sqrt{5} }{125} = - \frac{ \sqrt{5} }{25} [/tex]
[tex]c) \: ( - \sqrt{3} ) ^{ - 4} = ( - \frac{1}{ \sqrt{3} } ) ^{4} = ( - \frac{ \sqrt{3} }{3} ) ^{4} = \frac{9}{81} = \frac{1}{9} [/tex]
[tex]d) \: ( \sqrt{2} )^{ - 5} = ( \frac{1}{ \sqrt{2} } ) ^{5} = ( \frac{ \sqrt{2} }{2} ) ^{5} = \frac{4 \sqrt{2} }{32} = \frac{ \sqrt{2} }{8} [/tex]
[tex]e)(5 \sqrt{6}) ^{ - 2} = ( \frac{1}{5 \sqrt{6} } ) ^{2} = (\frac{ \sqrt{6} }{30} ) ^{2} = \frac{6}{900} = \frac{2}{300} = \frac{1}{150} [/tex]
[tex]f)( - 3 \sqrt{5} ) ^{ - 3} = ( - \frac{1}{3 \sqrt{5} } ) ^{3} = ( - \frac{ \sqrt{5} }{15} ) ^{3} = - \frac{5 \sqrt{5} }{3375} = - \frac{ \sqrt{5} }{675} [/tex]
