جواب کاردرکلاس صفحه 103 درس 7 ریاضی هشتم (توان و جذر)

\({({5^7})^4} = {5^{7 \times 4}} = {5^{28}}\)

\({\left[ {{{(\frac{2}{3})}^2}} \right]^3} = {(\frac{2}{3})^{2 \times 3}} = {(\frac{2}{3})^6}\)

\({\left[ {{{( - 6)}^2}} \right]^5} = {\left[ {{6^2}} \right]^5} = {6^{2 \times 5}} = {6^{10}}\)

\({\left[ {{{( - \frac{1}{7})}^3}} \right]^4} = {( - \frac{1}{7})^{3 \times 4}} = {( - \frac{1}{7})^{12}} = {(\frac{1}{7})^{12}}\)

\({({18^2})^7} = {18^{2 \times 7}} = {18^{14}}\)

\({({x^4})^8} = {x^{4 \times 8}} = {x^{32}}\)

\({\left[ {{{(ab)}^3}} \right]^2} = {(ab)^{3 \times 2}} = {(ab)^6}\)

\({(x{y^2})^3} = {x^3} \times {({y^2})^3} = {x^3}{y^6}\)

\({({2^m})^n} = {2^{m \times n}}\)

\(\begin{array}{l}{({3^2})^4} = {3^2} \times {3^4}\\\\\left\{ \begin{array}{l}{({3^2})^4} = {3^{2 \times 4}} = {3^8}\\\\{3^2} \times {3^4} = {3^{2 + 4}} = {3^6}\end{array} \right. \Rightarrow {({3^2})^4} \ne {3^2} \times {3^4}\\\end{array}\)

نادرست است.

\(\begin{array}{l}{3^5} \times {3^5} = {({3^5})^2}\\\\\left\{ \begin{array}{l}{3^5} \times {3^5} = {3^{5 + 5}} = {3^{10}}\\\\{({3^5})^2} = {3^{5 \times 2}} = {3^{10}}\end{array} \right. \Rightarrow {3^5} \times {3^5} = {({3^5})^2}\end{array}\)

درست است.

\(\begin{array}{l}{({3^2})^4} = {3^8}\\\\{({3^2})^4} = {3^{2 \times 4}} = {3^8}\end{array}\)

درست است.

\(\begin{array}{l}{({3^0})^2} = {3^2}\\\\{({3^0})^2} = {3^{0 \times 2}} = {3^0} \ne {3^2}\end{array}\)

نادرست است.

\(\begin{array}{l}{({5^3})^2} = {5^9}\\\\{({5^3})^2} = {5^{3 \times 2}} = {5^6} \ne {5^9}\end{array}\)

نادرست است.

\(\begin{array}{l}{3^2} \times {3^2} = {9^4}\\\\{3^2} \times {3^2} = {3^{2 + 2}} = {3^4} \ne {9^4}\end{array}\)

نادرست است.

\(\begin{array}{l}{3^5} \times {({2^2})^5} = {12^5}\\\\{3^5} \times {({2^2})^5} = {3^5} \times {4^5} = {(3 \times 4)^5} = {12^5}\end{array}\)

درست است.

\(\begin{array}{l}{a^2}.{a^0} = 1\\\\{a^2}.{a^0} = {a^{2 + 0}} = {a^2} \ne 1\end{array}\)

نادرست است.

\(\begin{array}{l}{({( - 2)^3})^2} = {2^6}\\\\{({( - 2)^3})^2} = {( - 2)^{3 \times 2}} = {( - 2)^6} = {2^6}\end{array}\)

درست است.

\(\begin{array}{l}( - {4^6}) = {4^6}\\\\( - {4^6}) = - {4^6} \ne {4^6}\end{array}\)

نادرست است.

\(\begin{array}{l}{\left[ {{{\left( { - 5} \right)}^2}} \right]^3} \times {\left( { - 5} \right)^2} = {\left( { - 5} \right)^{2 \times 3}} \times {\left( { - 5} \right)^2} = \\\\{\left( { - 5} \right)^6} \times {\left( { - 5} \right)^2} = {\left( { - 5} \right)^{6 + 2}} = {\left( { - 5} \right)^8}\end{array}\)

بنابراین گزینه الف درست است.

\({9^5} = {({3^2})^5} = {3^{10}}\)