Question

Find the quotient of ${100}^{100}+{50}^{50}$

Answer 1

${100}^{100}÷{50}^{50}$

$=\frac{{100}^{100}}{{50}^{50}}$

$=\frac{{(2\times 50)}^{100}}{{50}^{50}}$

$=\frac{2^{100}\times {50}^{100}}{{50}^{50}}$

$=2^{100}\times {50}^{(100-50)}$

$=2^{100}\times {50}^{50}$

$=2^{50}\times 2^{50}\times {50}^{50}$

$={(2\times 2\times 50)}^{50}$

$={\left(200\right)}^{50}$

Hece the quotient when ${100}^{100}$ is divided by ${50}^{50}$ is ${200}^{50}$.

Hence the correct answer is ${200}^{50}$.