Question
Evaluate: $\frac{7^{8}\text{a}^{10}\text{b}^{7}\text{c}^{12}}{7^{6}\text{a}^{8}\text{b}^{4}\text{c}^{12}}$
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Answer
We have, $\frac{7^{8}\text{a}^{10}\text{b}^{7}\text{c}^{12}}{7^{6}\text{a}^{8}\text{b}^{4}\text{c}^{12}}$ $=\Big(\frac{7^{8}}{7^{6}}\Big)\times\Big(\frac{\text{a}^{10}}{\text{a}^{8}}\Big)\times\Big(\frac{\text{b}^{7}}{\text{b}^{8}}\Big)\times\Big(\frac{\text{c}^{12}}{\text{c}^{12}}\Big)$ $7^{8-6}\times\text{a}^{10-8}\times\text{b}^{7-4}\times\text{c}^{12-12}$ $\Big[\because\frac{\text{a}^{\text{m}}}{\text{a}^{\text{n}}}=\text{a}^{\text{m-n}}\Big]$ $$ $7^{2}\times\text{a}^{2}\times\text{b}^{3}\times\text{c}^{0}=49\text{ a}^{2}\text{b}^{3}$ $\Big[\because\text{c}^{0}=1\Big]$
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