Calculați:3^1x3^2x3^3x...x3^20
![Calculați31x32x33xx320 class=](https://ro-static.z-dn.net/files/dbe/c60baafedd633ef6b9d0612694a49cd0.jpg)
[tex] {3}^{1} \times {3}^{2} \times {3}^{3} \times ... \times {3}^{20} = \\ {3}^{1 + 2 + 3 +... + 20} = \\ {3}^{20 \times 21 \div 2} = {3}^{210} [/tex]
[tex]\displaystyle\bf\\3^1\cdot3^2\cdot3^3\cdot ~...~\cdot 3^{20}=\\\\3^{1+2+3+...+20}\\\\1+2+3+...+20=\frac{20\cdot21}{2}=10\cdot21=210\\\\ 3^1\cdot3^2\cdot3^3\cdot ~...~\cdot 3^{20}=3^{1+2+3+...+20}=\boxed{\bf3^{210}}[/tex]