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1 با توجه به مثال های حل شده زیر، پاسخ موارد بعدی را به صورت یک عدد توان دار با توان طبیعی بنویسید:
الف \({5^{ - 2}} = \frac{1}{{{5^2}}} = \frac{1}{{25}} = {\left( {\frac{1}{5}} \right)^2}\)
ب \({\left( {\frac{2}{3}} \right)^{ - 2}} = \frac{1}{{{{\left( {\frac{2}{3}} \right)}^2}}} = \frac{1}{{\frac{4}{9}}} = \frac{9}{4} = {\left( {\frac{3}{2}} \right)^2}\)
ج \({\left( { - 6} \right)^{ - 3}} = \frac{1}{{\,\,\,\,\,\,\,}} = \frac{{\,\,\,\,\,\,\,}}{{\,\,\,\,\,\,\,}} = \)
د \({\left( { - \frac{2}{7}} \right)^{ - 4}} = \,\,\,\,\,\,\, = \,\,\,\,\,\, = \)
ج \({\left( { - 6} \right)^{ - 3}} = \frac{1}{{{{\left( { - 6} \right)}^{ - 3}}}} = \frac{1}{{108}} = - \frac{1}{{{6^3}}}\)
د \({\left( { - \frac{2}{7}} \right)^{ - 4}} = \frac{1}{{{{\left( { - \frac{2}{7}} \right)}^4}}} = \frac{1}{{\frac{8}{{2401}}}} = \frac{{2401}}{8} = {\left( { - \frac{7}{2}} \right)^4}\)
2 عبارت های برابر را مانند نمونه به هم وصل کنید : \(\left( {x \ne 0,y \ne 0} \right)\)
3 حاصل هر عبارت را به ساده ترین صورت بنویسید :
الف \({\left( { - \frac{1}{3}} \right)^{ - 4}} = \)
ب \({2^{ - 1}} + {3^{ - 1}} + {4^{ - 1}} = \)
ج \( - {\left( { - 5} \right)^2} = \)
د \( - {\left( { - 5} \right)^{ - 2}} = \)
هـ \( - {5^{ - 2}} = \)
و \({1^{ - 2}} = \)
ز \(\frac{{{{\left( { - 3} \right)}^0}}}{3} = \)
ح \( - \frac{1}{{{2^{ - 2}}}} = \)
ط \({\left( {\frac{2}{5}} \right)^{ - 2}} + {\left( {\frac{5}{2}} \right)^2} = \)
ی \({2^0} - {2^{ - 1}} = \)
الف \({\left( { - \frac{1}{3}} \right)^{ - 4}} = {\left( { - 3} \right)^4} = 81\)
ب \({2^{ - 1}} + {3^{ - 1}} + {4^{ - 1}} = \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{{6 + 4 + 3}}{{12}} = \frac{{13}}{{12}}\)
ج \( - {\left( { - 5} \right)^2} = - \left( { + 25} \right) = - 25\)
د \( - {\left( { - 5} \right)^{ - 2}} = - {\left( { - \frac{1}{5}} \right)^2} = - \frac{1}{{25}}\)
هـ \( - {5^{ - 2}} = - {\left( {\frac{1}{5}} \right)^2} = - \frac{1}{{25}}\)
و \({1^{ - 2}} = \frac{1}{{{1^2}}} = 1\)
ز \(\frac{{{{\left( { - 3} \right)}^0}}}{3} = \frac{1}{3}\)
ح \( - \frac{1}{{{2^{ - 2}}}} = \frac{1}{{{{\left( {\frac{1}{2}} \right)}^2}}} = 4\)
ط \({\left( {\frac{2}{5}} \right)^{ - 2}} + {\left( {\frac{5}{2}} \right)^2} = {\left( {\frac{5}{2}} \right)^2} + {\left( {\frac{5}{2}} \right)^2} = \frac{{25}}{4} + \frac{{25}}{4} = \frac{{50}}{4}\)
ی \({2^0} - {2^{ - 1}} = 1 - \frac{1}{2} = \frac{1}{2}\)
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