Question
Evaluate: $\frac{125\times5^{2}\times\text{a}^{7}}{10^{3}\times\text{a}^{4}}$
✓
Answer
We have, $\frac{125\times5^{2}\times\text{a}^{7}}{10^{3}\times\text{a}^{4}}$ $\frac{5^{3}\times5^{2}\times\text{a}^{7}}{(2\times5)^{3}\times\text{a}^{4}}$ $\Big[\because 125=5^{3}\Big]$ $\frac{5^{2+3}\times\text{a}^{7}}{2^{3}\times5^{3}\times\text{a}^{4}}$ $\Big[\because\text{a}^{\text{m}}\times\text{a}^{\text{n}}=\text{a}^{\text{m+n}}\text{ and }(\text{a}\times\text{b})^{ \text{m}}=\text{a}^{\text{m}}\times\text{b}^{\text{m}}\Big]$ $\frac{5^{5}\times\text{a}^{7}}{2^{3}\times5^{3}\times\text{a}^{4}}$ $=\Big(\frac{5^{5}}{5^{3}}\Big)\times\Big(\frac{\text{a}^{7}}{\text{a}^{4}}\Big)\times\Big(\frac{1}{2^{3}}\Big)$ $\frac{5^{5-3}\times\text{a}^{7-4}}{2^{3}}$ $\Big[\because\frac{\text{a}^{\text{m}}}{\text{a}^{\text{n}}}=\text{a}^{\text{m-n}}\Big]$ $\frac{5^{2}\times\text{a}^{3}}{2^{3}}=\frac{25\text{a}^{3}}{8}$
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