گام به گام تمرین صفحه 108 درس 7 ریاضی هشتم (توان و جذر)

\(\begin{array}{l}81 = {3^4}\\\\ - 8 = {( - 2)^3}\\\\1024 = {2^{10}}\\\\ - \frac{{125}}{{729}} = {( - \frac{5}{9})^3}\\\\\frac{1}{{512}} = {(\frac{1}{2})^9}\\\\ - \frac{1}{{32}} = {( - \frac{1}{2})^5}\end{array}\)

\(\begin{array}{l}{(\frac{{ - 5}}{2})^2} = - \frac{{25}}{4}\\\\{(\frac{{ - 5}}{2})^2} = \frac{{25}}{4} \ne - \frac{{25}}{4}\end{array}\)

نادرست است

\(\begin{array}{l}{(\frac{5}{{11}})^0} = 0\\\\{(\frac{5}{{11}})^0} = 1 \ne 0\end{array}\)

نادرست است

\(\begin{array}{l}{\left[ {{{(\frac{2}{3})}^3}} \right]^5} = {(\frac{2}{3})^8}\\\\{\left[ {{{(\frac{2}{3})}^3}} \right]^5} = {(\frac{2}{3})^{3 \times 5}} = {(\frac{2}{3})^{15}} \ne {(\frac{2}{3})^8}\end{array}\)

نادرست است

\(\begin{array}{l}{(\frac{2}{7})^4} \times {(\frac{3}{5})^0} = {(\frac{2}{7})^4}\\\\{(\frac{2}{7})^4} \times {(\frac{3}{5})^0} = {(\frac{2}{7})^4} \times 1 = {(\frac{2}{7})^4}\end{array}\)

درست است

\(\begin{array}{l}{10^3} \times {10^4} = {10^{12}}\\\\{10^3} \times {10^4} = {10^{3 + 4}} = {10^7} \ne {10^{12}}\end{array}\)

نادرست است

\(\begin{array}{l}{( - 2)^3} \times ( - 2) = 16\\\\{( - 2)^3} \times ( - 2) = ( - 8) \times ( - 2) = 16\end{array}\)

درست است

\(\begin{array}{l}{(\frac{1}{3})^4} \times {3^{10}} = \frac{{{3^{10}}}}{{{3^4}}} = {3^{10 - 4}} = {3^6}\\\\\frac{{{5^6} \times {6^3}}}{{{5^4} \times {6^5}}} = \frac{{{5^6}}}{{{5^4}}} \times \frac{{{6^3}}}{{{6^5}}} = {5^2} \times \frac{1}{{{6^2}}} = \frac{{{5^2}}}{{{6^2}}} = {(\frac{5}{6})^2}\\\\\frac{{{x^7} \times {y^4}}}{{{x^5} \times {y^2}}} = \frac{{{x^7}}}{{{x^5}}} \times \frac{{{y^4}}}{{{y^2}}} = {x^2} \times {y^2} = {(xy)^2}\end{array}\)

\(\begin{array}{l}{3^5} \times {3^\bigcirc } = {3^9} \Rightarrow {3^5} \times {3^4} = {3^9}\\\\{({7^4})^\bigcirc } = {7^8} \Rightarrow {({7^4})^2} = {7^8}\\\\\frac{{{7^\bigcirc } \times {7^2}}}{{{7^3}}} = {7^5} \Rightarrow \frac{{{7^6} \times {7^2}}}{{{7^3}}} = {7^5}\\\\{(\frac{2}{3})^\bigcirc } \div {(\frac{2}{3})^5} = {(\frac{2}{3})^2} \Rightarrow {(\frac{2}{3})^7} \div {(\frac{2}{3})^5} = {(\frac{2}{3})^2}\\\\\frac{{{{( - 6)}^8}}}{{{{( - 6)}^\bigcirc }}} = {( - 6)^3} \Rightarrow \frac{{{{( - 6)}^8}}}{{{{( - 6)}^5}}} = {( - 6)^3}\end{array}\)

\( \Rightarrow - {4^3}\,,\,{( - 1)^5}\,,\,0\,,\,{(\frac{1}{2})^5}\,,\,{1^{12}}\,,\,{6^5}\)

\(\begin{array}{l}{(\sqrt 5 )^2} = 25\\\\{(\sqrt 5 )^2} = 5 \ne 25\end{array}\)

نادرست است

\({(\sqrt 5 )^2} = 5\)

درست است

\(\begin{array}{l}{(\sqrt 5 )^2} = {( - \sqrt 5 )^2}\\\\{(\sqrt 5 )^2} = 5 = {( - \sqrt 5 )^2}\end{array}\)

درست است

\(\begin{array}{l} + \sqrt 5 = - \sqrt 5 \\\\ + \sqrt 5 \ne - \sqrt 5 \end{array}\)

نادرست است

\({( - {10^2})^3} = - {10^6}\)

\({\left[ {{{( - 10)}^2}} \right]^3} = {10^6}\)

\({({x^2}{y^3})^4} = {x^8}{y^{12}}\)

\({(\frac{{{x^7}}}{{{x^3}}})^5} = {({x^4})^5} = {x^{20}}\)

\(\begin{array}{l}\left[ {{{36}^5} \div {{( - 3)}^5}} \right] \div \left[ {{{( - 2)}^5} \times {{( - 3)}^5}} \right] = \\\\\frac{{\frac{{{{36}^5}}}{{{{( - 3)}^5}}}}}{{\left[ {{{( - 2)}^5} \times {{( - 3)}^5}} \right]}} = \frac{{{{\left( {\frac{{36}}{{ - 3}}} \right)}^5}}}{{{{\left[ {( - 2) \times ( - 3)} \right]}^5}}} = \\\\\frac{{{{( - 12)}^5}}}{{{6^5}}} = {(\frac{{ - 12}}{6})^5} = {( - 2)^5}\end{array}\)

\({2^9}\) نصف  \( = \frac{1}{2} \times {2^9} = \frac{{{2^9}}}{2} = {2^8}\)

\({4^7}\) ربع  \( = \frac{1}{4} \times {4^7} = \frac{{{4^7}}}{4} = {4^6}\)