question_answer 1)

                Find the product:                 (i) \[({{a}^{2}})\times (2{{a}^{22}})\times (4{{a}^{26}})\] (ii) \[\left( \frac{2}{3}xy \right)\times \left( \frac{-9}{10}{{x}^{2}}{{y}^{2}} \right)\] (iii) \[\left( -\frac{10}{3}\,p{{q}^{3}} \right)\,\times \left( \frac{6}{5}\,{{p}^{3}}q \right)\] (iv) \[x\times {{x}^{2}}\times {{x}^{3}}\times {{x}^{4}}\].

Answer:

                \[({{a}^{2}})\times (2{{a}^{22}})\times (4{{a}^{26}})\] \[({{a}^{2}})\times (2{{a}^{22}})\times (4{{a}^{26}})\] \[=(2\times 4)\times ({{a}^{2}}\times {{a}^{22}}\times {{a}^{26}})\] \[=8\times {{a}^{50}}=8{{a}^{50}}\]. (ii) \[\left( \frac{2}{3}xy \right)\times \,\left( -\frac{9}{10}{{x}^{2}}{{y}^{2}} \right)\] \[\left( \frac{2}{3}xy \right)\times \,\left( -\frac{9}{10}{{x}^{2}}{{y}^{2}} \right)\] \[=\left\{ \frac{2}{3}\times \,\left( -\frac{9}{10} \right) \right\}\times (x\times {{x}^{2}})\times (y\times {{y}^{2}})\] \[=-\frac{3}{5}\,{{x}^{3}}{{y}^{3}}\]. (iii) \[\left( -\frac{10}{3}p{{q}^{3}} \right)\times \,\left( \frac{6}{5}{{p}^{3}}q \right)\] \[\left( -\frac{10}{3}p{{q}^{3}} \right)\times \,\left( \frac{6}{5}{{p}^{3}}q \right)\] \[=\left\{ \left( -\frac{10}{3} \right)\times \frac{6}{5} \right\}\times (p\times {{p}^{3}})\times ({{p}^{3}}\times q)\] \[=-4{{p}^{4}}{{q}^{4}}\]. (iv) \[x\times {{x}^{2}}\times {{x}^{3}}\times {{x}^{4}}\] \[x\times {{x}^{2}}\times {{x}^{3}}\times {{x}^{4}}\]\[={{x}^{1}}\times {{x}^{2}}\times {{x}^{3}}\times {{x}^{4}}\] \[={{x}^{1+2+3+4}}\] \[={{x}^{10}}\].