• # question_answer 9)                 Obtain the product of                 (i) $xy,\,yz,\,zx$                 (ii) $a,\,-{{a}^{2}},\,{{a}^{3}}$                 (iii) $2,\,4y,\,8{{y}^{2}},\,16{{y}^{3}}$                 (iv) $a,\,2b,\,3c,\,6abc$                 (v) $m,\,-mn,\,mnp$.

(i) $xy,\,yz,\,zx$ Required product $=(xy)\times (yz)\times (zx)$ $=(x\times x)\times (y\times y)\times (z\times z)$ $={{x}^{2}}\times {{y}^{2}}\times {{z}^{2}}$ $={{x}^{2}}{{y}^{2}}{{z}^{2}}$                 (ii) $a,\,-{{a}^{2}},\,{{a}^{3}}$ Required product $=(a)\times \,(-{{a}^{2}})\,\times ({{a}^{3}})$ $=-(a\times {{a}^{2}}\times {{a}^{3}})$ $=-{{a}^{6}}$                 (iii) $2,\,4y,\,8{{y}^{2}},\,16{{y}^{3}}$ Required product $=(2)\times (4y)\times (8{{y}^{2}})\times (16{{y}^{3}})$ $=(2\times 4\times 8\times 16)\times (y\times {{y}^{2}}\times {{y}^{3}})$ $=1024{{y}^{6}}$ (iv) $a,\,2b,\,3c,\,6abc$ Required product $=(a)\times (2b)\times (3c)\times (6abc)$ $=(2\times 3\times 6)\times (a\times a)\times (b\times b)$$\times (c\times c)$ $=36{{a}^{2}}{{b}^{2}}{{c}^{2}}$ (v) $m,\,-mn,\,mnp$ Required product $=(m)\times (-mn)\times (mnp)$ $=(-1)\times (m\times m\times m)$$\times (n\times n)\times p$ $=-{{m}^{3}}{{n}^{2}}p$.