• # question_answer12)                 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) $x\times {{x}^{2}}\times {{x}^{3}}\times {{x}^{4}}$.

$({{a}^{2}})\times (2{{a}^{22}})\times (4{{a}^{26}})$ $({{a}^{2}})\times (2{{a}^{22}})\times (4{{a}^{26}})$ $=(2\times 4)\times ({{a}^{2}}\times {{a}^{22}}\times {{a}^{26}})$ $=8\times {{a}^{50}}=8{{a}^{50}}$. (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}}$ $={{x}^{1+2+3+4}}$ $={{x}^{10}}$.