Question
Evaluate: $\frac{5^{4}\times7^{4}\times2^{7}}{8\times49\times5^{3}}$
✓
Answer
We have, $\frac{5^{4}\times7^{4}\times2^{7}}{8\times49\times5^{3}}$ $\frac{5^{4}\times7^{4}\times2^{7}}{2^{3}\times7^{2}\times5^{3}}$ $\Big[\because8=2^{3}\text{ and }49=7^{2}\Big]$ $=\Big(\frac{5^{4}}{5^{3}}\Big)\times\Big(\frac{2^{7}}{2^{3}}\Big)\times\Big(\frac{7^{4}}{7^{2}}\Big)$ $\Big[\because\frac{\text{a}^{\text{m}}}{\text{a}^{\text{n}}}=\text{a}^{\text{m-n}}\Big]$ $=5^{4}\times2^{7-3}\times7^{7-2}$ $=5\times2^{4}\times7$ $=5\times16\times49=3920$
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