Answer:
(i) \[28{{x}^{4}}\div 56x\] \[28{{x}^{4}}\div 56x\] \[=\frac{28{{x}^{4}}}{56x}\] \[=\frac{2\times 2\times 7\times x\times x\times x\times x}{2\times 2\times 2\times 7\times x}\] \[=\frac{x\times x\times x}{2}=\frac{{{x}^{3}}}{2}\] (ii) \[-36{{y}^{3}}\div 9{{y}^{2}}\] \[-36{{y}^{3}}\div 9{{y}^{2}}\] \[=\frac{-36{{y}^{3}}}{9{{y}^{2}}}\] \[=\frac{-2\times 2\times 3\times 3\times y\times y\times y}{3\times 3\times y\times y}\] \[=-2\times 2\times y=-4y\] (iii) \[66p{{q}^{2}}{{r}^{3}}\div \,11q{{r}^{2}}\] \[66p{{q}^{2}}{{r}^{3}}\div \,11q{{r}^{2}}\] \[=\frac{66p{{q}^{2}}{{r}^{3}}}{11q{{r}^{2}}}\] \[=\frac{2\times 3\times 11\times p\times q\times q\times r\times r\times r}{11\times q\times r\times r}\] \[=2\times 3\times p\times q\times r\] \[=6pqr\] (iv) \[34{{x}^{3}}{{y}^{3}}{{z}^{3}}\div \,51x{{y}^{2}}{{z}^{3}}\] \[34{{x}^{3}}{{y}^{3}}{{z}^{3}}\div \,51x{{y}^{2}}{{z}^{3}}\] \[=\frac{34{{x}^{3}}{{y}^{3}}{{z}^{3}}}{51x{{y}^{2}}{{z}^{3}}}\] \[=\frac{2\times 17\times x\times x\times x\times y\times y\,\times y\times z\times z\times z}{3\times 17\times x\times y\times y\times z\times z\times z}\] (v) \[12{{a}^{8}}{{b}^{8}}\div \,(-6{{a}^{6}}{{b}^{4}})\] \[12{{a}^{8}}{{b}^{8}}\div \,(-6{{a}^{6}}{{b}^{4}})\] \[=\frac{12{{a}^{8}}{{b}^{8}}}{-6{{a}^{6}}{{b}^{4}}}\] \[=\frac{\begin{align} & 2\times 2\times 3\times a\times a\times a\times a\times a\times a\times a \\ & \,\,\,\,\,\,\,\,\times a\times b\times b\times b\times b\times b\times b\times b\times b \\ \end{align}}{\begin{align} & -2\times 3\times a\times a\times a\times a\times a\times a\times b \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\times b\times b\times b \\ \end{align}}\]\[=-2\times a\times a\times b\times b\times b\times b\] \[=-2{{a}^{2}}{{b}^{4}}\]
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