جواب یاداوری صفحه 102 درس 7 ریاضی هشتم (توان و جذر)

\({2^6} \times {2^3} = {2^{6 + 3}} = {2^9}\)

\({\left( { - \frac{2}{3}} \right)^7} \times {\left( { - \frac{2}{3}} \right)^5} = {\left( { - \frac{2}{3}} \right)^{7 + 5}} = {\left( { - \frac{2}{3}} \right)^{12}}\)

\({8^3} \times {2^3} = {8^3} \times 8 = {8^{3 + 1}} = {8^4}\)

\({\left( { - 6} \right)^4} \times {\left( {\frac{1}{2}} \right)^4} = {\left( { - 6 \times \frac{1}{2}} \right)^4} = {\left( { - 3} \right)^4}\)

\(\begin{array}{l}{2^5} \times {3^2} \times {6^5} \times {4^2} = {(2 \times 6)^5} \times {(3 \times 4)^2} = \\\\{12^5} \times {12^2} = {12^{5 + 2}} = {12^7}\end{array}\)

\(3 \times {\left( {\frac{3}{5}} \right)^0} \times 81 = 3 \times 1 \times {3^4} = {3^{1 + 4}} = {3^5}\)

\(36 \times 144 = {6^2} \times {12^2} = {(6 \times 12)^2} = {72^2}\)

\(\begin{array}{l}{2^3} \times {8^5} \times {4^3} = {2^3} \times {({2^3})^5} \times {({2^2})^3} = \\\\{2^3} \times {2^{15}} \times {2^6} = {2^{3 + 15 + 6}} = {2^{24}}\end{array}\)

\({a^2} \times {a^8} = {a^{2 + 8}} = {a^{10}}\)

\({x^4} \times {y^4} = {(xy)^4}\)

\(\begin{array}{l}{\left( {ab} \right)^5} \times {a^3} \times {b^4} = {a^5} \times {b^5} \times {a^3} \times {b^4} = \\\\{a^{5 + 3}} \times {b^{5 + 4}} = {a^8} \times {b^9}\end{array}\)

\({\left( {xy} \right)^4} \times {\left( {xy} \right)^7} = {\left( {xy} \right)^{4 + 7}} = {\left( {xy} \right)^{11}}\)

\(\begin{array}{l}125 \times {18^3} \times {\left( {\frac{1}{9}} \right)^3} = {5^3} \times {18^3} \times {\left( {\frac{1}{9}} \right)^3} = \\\\{\left( {5 \times 18 \times \frac{1}{9}} \right)^3} = {10^3}\end{array}\)

\(\begin{array}{l}8a \times {\left( {2a} \right)^3} \times 2{a^3} = {2^3}a \times {2^3}{a^3} \times 2{a^3} = \\\\{2^{3 + 3 + 1}}{a^{1 + 3 + 3}} = {2^7}{a^7} = {\left( {2a} \right)^7}\end{array}\)

\(\begin{array}{l}{18^5} = {\left( {6 \times 3} \right)^5}\\\\{a^8} = {a^3} \times {a^5}\\\\70 \times {4^5} = {4^5}\\\\{\left( { - \frac{7}{2}} \right)^7}\; \times \;{\left( { - \frac{7}{2}} \right)^2} = {\left( { - \frac{7}{2}} \right)^9}\\\\{\left( {4 \times 3} \right)^6} = {4^6} \times {3^6}\end{array}\)