Question

Question 85 (e)

Evaluate
${\left(\frac{6\times 10}{2^2\times 5^3}\right)}^2\times \frac{25}{27}$

Answer 1

We have
${\left(\frac{6\times 10}{2^2\times 5^3}\right)}^2\times \frac{25}{27}={\left(\frac{2\times 3\times 2\times 5}{2^2\times 5^3}\right)}^2\times \frac{5^2}{3^3}=\left(\frac{2^2\times 3\times 5}{2^2\times 5^3}\right)\times \frac{5^2}{3^3}={\left(\frac{3}{5^2}\right)}^2\times \frac{5^2}{3^3}=\frac{3^2}{5^4}\times \frac{5^2}{3^3}=\frac{1}{5^2\times 3}=\frac{1}{25\times 3}=\frac{1}{75}$