O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Chapter: Exponents, Exercise 3: Exercise

If $x={\left[{\left(\frac{2}{3}\right)}^2\right]}^3\times {\left(\frac{1}{3}\right)}^{-2}\times 3^{-1}\times \frac{1}{6}$, find the reciprocal of $x$. (Write the answer as proper/improper fraction)

Reciprocal of ${\left({\left(\frac{8}{11}\right)}^2\right)}^{-5}\times {\left(\frac{11}{8}\right)}^{-12}={\left(\frac{11}{8}\right)}^m$. Find $m$.

If the reciprocal of ${\left(-\frac{3}{7}\right)}^{-3}÷{\left(-\frac{3}{7}\right)}^{-4}=\frac{k}{3}$, then find the value of $k$.

Find the reciprocal of $\left[{\left(\frac{1}{3}\right)}^{-3}-{\left(\frac{1}{2}\right)}^{-3}\right]÷{\left(\frac{1}{4}\right)}^{-3}$. (Give answer as improper fraction)

Simplify: $\left[{\left(-\frac{1}{3}\right)}^8÷{\left(-\frac{1}{3}\right)}^5\right]-\left[{\left(-\frac{1}{3}\right)}^5÷{\left(-\frac{1}{3}\right)}^3\right]$

Simplify: ${\left(2^{-1}÷5^{-1}\right)}^2\times {\left(\frac{-5}{8}\right)}^{-2}$

If $\frac{a}{b}={\left(\frac{2}{3}\right)}^{-2}÷{{\left[{\left(\frac{-2}{3}\right)}^6\right]}^0}^{}$, then the value of ${\left(\frac{a}{b}\right)}^{-3}$ is

Find $x$ so that ${\left[{\left\{{\left(\frac{4}{57}\right)}^8\right\}}^3\right]}^{-2}={\left(\frac{4}{57}\right)}^{-5x-3}$.