Evaluate: (6 10 2^ 2 5^ 3 )^ 2 25 27 - Vidyadip

Question

Evaluate:
$\Big(\frac{6\times10}{2^{2}\times5^{3}}\Big)^{2}\times\frac{25}{27}$

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Answer

We have, $\Big(\frac{6\times10}{2^{2}\times5^{3}}\Big)^{2}\times\frac{25}{27}$
$=\Big(\frac{2\times3\times2\times5}{2^{2}\times5^{3}}\Big)^{2}\times\frac{5^{2}}{3^{2}}$ $\Big[\because 6=2\times3\text{ and }10=2\times5\Big]$
$\Big(\frac{2^{2}\times3\times5}{2^{2}\times5^{3}}\Big)^{2}\times\frac{5^{2}}{5^{3}}$ $\Big[\because(\text{a}\times\text{b})^{ \text{m}}=\text{a}^{\text{m}}\times\text{b}^{\text{m}}\Big]$
$$$=\Big(\frac{3}{5^{2}}\Big)^{2}\times\frac{5^{2}}{3^{3}}$
$=\frac{3^{2}}{5^{4}}\times\frac{5^{2}}{3^{3}}$$\Big[\because(\text{a}^{\text{m}})^{\text{n}}=\text{a}^{\text{mn}}\Big]$
$=\frac{1}{5^{2}\times3}=\frac{1}{25\times3}=\frac{1}{75}$

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