R. S. Aggarwal Solutions for Chapter: Simplification, Exercise 2: EXERCISE 4B

Evaluate: ${\left\{\frac{1\times 3\times 9+2\times 6\times 18+3\times 9\times 27+\dots }{1\times 5\times 25+2\times 10\times 50+3\times 15\times 75+\dots .}\right\}}^{\frac{1}{3}}$

Simplify:$\frac{7}{5-\frac{8}{3}}÷\frac{3-\frac{3}{2}}{4-\frac{3}{2}}-\frac{5}{7} \mathrm{of} \left\{\frac{1}{1\frac{3}{7}}+\frac{6}{5}\right.\mathrm{of} \left.\frac{3\frac{1}{3}-2\frac{1}{2}}{\frac{47}{21}-2}\right\}$.

Simplify: $1\frac{1}{2} \mathrm{of} \left(\frac{3}{4}÷\frac{7}{8}\right)+\frac{1}{2}÷\left[2\frac{4}{5}-\left\{\frac{2}{3}÷\left(\frac{1}{2}+\frac{1}{3}-\overline{\frac{1}{3}+\frac{1}{4}}\right)\right\}\right]$

Simplify: $\mathrm{9}\frac{1}{2}+\frac{3}{2}÷\frac{1}{2} \mathrm{of} \frac{5}{4}-\frac{3}{5}\times 2\frac{1}{3}÷1\frac{5}{7} \mathrm{of} \left(3\frac{1}{2}-2\frac{1}{3}\right)$

Evaluate:$\frac{\left(4\times 4-3\times 3\right)+\left(4\times 4\times 4+3\times 3\times 3\right)}{\left(4\times 4-3\times 3\right)}.$

Simplify: $1+\frac{1}{1+\frac{1}{1-\frac{1}{6}}}$

Simplify: $\frac{1}{2+\frac{1}{2+\frac{1}{2-\frac{1}{2}}}}$

Simplify: $1-\frac{5}{7+\frac{1}{4+\frac{1}{2+\frac{1}{3}}}}$