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حاصل هریک از عبارت های زیر را به صورت یک عبارت توان دار بنویسید: \(\left( {b,x,y \ne 0} \right)\)
\(\begin{array}{l}{5^{ - 7}} \times {5^{10}} = \\\\\\{\left( {\frac{{ - 3}}{8}} \right)^4} \times {\left( {\frac{{ - 3}}{8}} \right)^{ - 9}}\\\\\\{b^{ - 2}} \times {b^{ - 3}} = \\\\\\{\left( { - 4} \right)^{ - 9}} \times {\left( { - 4} \right)^{ - 1}} = \\\\\\{\left( {\sqrt 2 } \right)^4} \times {\left( {\sqrt 2 } \right)^{ - 2}} = \\\\\\{\left( {\frac{x}{y}} \right)^{ - 7}} \times {\left( {\frac{x}{y}} \right)^{11}} = \end{array}\)
\(\begin{array}{l}{5^{ - 7}} \times {5^{10}} = {5^3}\\\\\\{\left( { - \frac{3}{8}} \right)^4} \times {\left( { - \frac{3}{8}} \right)^{ - 9}} = {\left( { - \frac{3}{8}} \right)^{ - 5}} = {\left( { - \frac{8}{3}} \right)^5}\;\\\\\\{b^{ - 2}} \times {b^{ - 3}} = {b^{ - 5}} = {\left( {\frac{1}{b}} \right)^5}\\\\\\{\left( { - 4} \right)^{ - 9}} \times {\left( { - 4} \right)^{ - 1}} = {\left( { - 4} \right)^{ - 10}} = {\left( {\frac{1}{4}} \right)^{10}}\\\\\\{\left( {\sqrt 2 } \right)^4} \times {\left( {\sqrt 2 } \right)^{ - 2}} = {\left( {\sqrt 2 } \right)^2} = 2\\\\\\{\left( {\frac{x}{y}} \right)^{ - 7}} \times {\left( {\frac{x}{y}} \right)^{ - 11}} = {\left( {\frac{x}{y}} \right)^4}\end{array}\)
نکات تکمیلی
\({({a^m})^n} = {a^{mn}}\,\,\,,\,\,\,\,a \ne 0\,\,\,,\,\,\,m,n \in \mathbb{Z}\)
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