\(\dfrac{6^{100}\cdot18^{100}\cdot49^{50}}{14^{100}\cdot27^{100}\cdot4^{50}}\)
\(=\dfrac{3^{100}\cdot2^{100}\cdot\left(3^2\right)^{100}\cdot2^{100}\cdot\left(7^2\right)^{60}}{7^{100}\cdot2^{100}\cdot\left(3^3\right)^{100}\cdot\left(2^2\right)^{50}}\)
\(=\dfrac{3^{100}\cdot3^{200}\cdot2^{100}\cdot7^{120}}{7^{100}\cdot3^{300}\cdot2^{100}}\)
\(=\dfrac{3^{200}\cdot7^{20}}{3^{200}}\)
\(=7^{20}\)
Giải:
\(\dfrac{6^{100}.18^{100}.49^{50}}{14^{100}.27^{100}.4^{50}}.\)
\(=\dfrac{\left(3.2\right)^{100}.\left(3^2.2\right)^{100}.\left(7^2\right)^{50}}{\left(2.7\right)^{100}.\left(3^3\right)^{100}.\left(2^2\right)^{50}}.\)
\(=\dfrac{3^{100}.2^{100}.\left(3^2\right)^{100}.2^{100}.\left(7^2\right)^{50}}{2^{100}.7^{100}.\left(3^3\right)^{100}.\left(2^2\right)^{100}}.\)
\(=\dfrac{3^{100}.\left(3^2\right)^{100}.2^{100}.7^{100}}{7^{100}.\left(3^3\right)^{100}.2^{100}.2^{100}}.\)
\(=\dfrac{\left(3^3\right)^{100}}{\left(3^3\right)^{100}.2^{100}}.\)
\(=\dfrac{1}{2^{100}}.\)
Vậy.....
~ Học tốt!!! ~
P/s: mik ko bt có đúg hay ko vì phép tính này hơi nhìu lũy thừa và hơi "nhì nhằng", nên mik có sai ở đâu thì bn thông cảm nhé!!!
Nam Nguyễn