How many times is $3^{20} + 3^{22}$ greater than $3^{20}$

Question

I just don't know where to start any help is appreciated.

Answer 1

Hint. Factor $3^{20}+3^{22}$ as $3^{20}(1+3^2)$.

Answer 2

This question is tricky in the wordings. Consider $$\frac{3^{20}+3^{22}}{3^{20}} = \frac{3^{20}(1+3^2)}{3^{20}} = 1+3^2 = 10$$ Hence, $3^{20}+3^{22}$ is 10 times of $3^{20}$. So, $3^{20}+3^{22}$ is $\mathbf {greater}$ than $3^{20}$ by $$10-1=9\; \text{times}$$