\(\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}=\dfrac{x+y+z}{a+b+c}=x+y+z\)
\(\Rightarrow\left(x+y+z\right)^{2020}=\dfrac{x^{2020}}{a^{2020}}=\dfrac{y^{2020}}{b^{2020}}=\dfrac{z^{2020}}{c^{2020}}=\dfrac{x^{2020}+y^{2020}+z^{2020}}{a^{2020}+b^{2020}+c^{2020}}=x^{2020}+y^{2020}+z^{2020}\)