Solve $-0.2^{2019} \times 5^{2020} $ without calculator

Question

This is a question extracted by my Mathematics test and I got wrong on it because my calculator cannot solve problems that huge. I want to know how to solve the question above without calculator.

Don't know which tag should be used, sorry!

Answer 1

So first you multiply $-0.2^{2019}\cdot{5}^{2020}$ by $-0.2$. And whatever number you get from that, you can divide it by $-0.2$ to get the result.

$-0.2^{2020}\cdot{5}^{2020}$ is equal to $(-1)^{2020}$ (you can multiply bases of exponents if they are raised to the same power) and $(-1)^{2020}$ is equal to $1$. And $1$ divided by $-0.2$ is equal to $-5$.

Answer 2

$$-0.2^{2019}\times 5^{2020} =\frac{-0.2^{2020}\times5^{2020}}{0.2}= \frac{-(0.2\times 5)^{2020}}{0.2}=\frac{-1^{2020}}{0.2}=\frac{-1}{0.2}=-5$$