question_answer 9)

                Carry out the following divisions:                 (i) \[28{{x}^{4}}\div 56x\]                 (ii) \[-36{{y}^{3}}\div 9{{y}^{2}}\]                 (iii) \[66p{{q}^{2}}{{r}^{3}}\div \,11q{{r}^{2}}\]                 (iv) \[34{{x}^{3}}{{y}^{3}}{{z}^{3}}\div \,51x{{y}^{2}}{{z}^{3}}\]                 (v) \[12{{a}^{8}}{{b}^{8}}\div \,(-6{{a}^{6}}{{b}^{4}})\]

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) \[12{{a}^{8}}{{b}^{8}}\div \,(-6{{a}^{6}}{{b}^{4}})\]                 \[12{{a}^{8}}{{b}^{8}}\div \,(-6{{a}^{6}}{{b}^{4}})\] \[=\frac{12{{a}^{8}}{{b}^{8}}}{-6{{a}^{6}}{{b}^{4}}}\] \[=\frac{\begin{align}   & 2\times 2\times 3\times a\times a\times a\times a\times a\times a\times a \\  & \,\,\,\,\,\,\,\,\times a\times b\times b\times b\times b\times b\times b\times b\times b \\ \end{align}}{\begin{align}   & -2\times 3\times a\times a\times a\times a\times a\times a\times b \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\times b\times b\times b \\ \end{align}}\]\[=-2\times a\times a\times b\times b\times b\times b\] \[=-2{{a}^{2}}{{b}^{4}}\]