\(3^{2021}=3^{2020}\cdot3=\overline{...1}\cdot3=\overline{...3}\)
\(7^{2022}=7^{2020}\cdot7^2=\overline{...1}\cdot49=\overline{...9}\)
\(13^{2023}=13^{2020}\cdot13^3=\overline{...1}\cdot\overline{...7}=\overline{...7}\)
\(\Rightarrow3^{2021}\cdot7^{2022}\cdot13^{2023}=\overline{...3}\cdot\overline{...9}\cdot\overline{...7}=\overline{...9}\)
Vậy chữ số hàng đơn vị của tích trên là 9
\(B=3^{2021}.7^{2022}.13^{2023}\)
\(=3^{2020}.3.7^{2020}.7^2.13^{2020}.13^3\)
\(=\left(3^4\right)^{505}.3.\left(7^4\right)^{505}.49.\left(13^4\right)^{505}.2197\)
\(=\overline{\left(...1\right)}^{505}.3.\overline{\left(...1\right)}^{505}.49.\overline{\left(...1\right)}^{505}.2197\)
\(=\overline{\left(...1\right)}.3.\overline{\left(...1\right)}.49.\overline{\left(...1\right)}.2197\)
\(=\overline{\left(...3\right)}.\overline{\left(...9\right)}.\overline{\left(...7\right)}\)
\(=\overline{...9}\)
