The quotient when 10100 is divided by 575 is

Answer: Option D

$$\begin{array}{rl}& \text{Expression,}\\ & \text{ = }\frac{{\left(10\right)}^{100}}{{\left(5\right)}^{75}}\\ & =\frac{{\left(2\times 5\right)}^{100}}{{\left(5\right)}^{75}}\\ & =\frac{{\left(2\right)}^{100}\times {\left(5\right)}^{100}}{{\left(5\right)}^{75}}\\ & =2^{100}\times \frac{5^{100}}{5^{75}}\\ & =2^{100}\times 5^{\left(100-75\right)}.....\left[\because \frac{a^m}{a^n}=a^{m-n}\right]\\ & =2^{100}\times 5^{25}\\ & =2^{25}\times 5^{25}\times 2^{75}.....\left[\because a^m\times a^n=a^{m+n}\right]\\ & ={\left(10\right)}^{25}\times 2^{75}.....\left[\because a^m\times b^m=a{b}^m\right]\end{array}$$