Vaishali Bhatia and Rupesh Pathak Solutions for Chapter: Exponents, Exercise 7: HOTS

If ${\left(\frac{2}{11}\right)}^{x-1}={\left(\frac{11}{2}\right)}^{x-5}$, then find $x$.

Simplify the following: $\frac{2^{x-3}\times 4^{b-4}\times 5^2}{2^{x-5}\times 4^{b-5}\times 5}$

Simplify the following: $\frac{1}{1+x^{a-b}}+\frac{1}{1+x^{b-a}}$

Radius of planet $A$ is about $21800 \mathrm{km}$. Radius of planet $B$ is ${10}^7$ times the radius of planet $A$.Find the radius of planet $B$ and express the answer in standard form.