c,\(\dfrac{4^{30}.3^{43}}{2^{57}.27^{15}}=\dfrac{\left(2^2\right)^{30}.3^{43}}{2^{57}.\left(3^3\right)^{15}}=\dfrac{2^{60}.3^{43}}{2^{57}.3^{45}}=\dfrac{2^3}{3^2}=\dfrac{8}{9}\)
a) \(\left(\dfrac{5}{3}-\dfrac{1}{2}\right):\left(\dfrac{3}{4}-\dfrac{5}{2}\right)\)
\(=\left(\dfrac{10}{6}-\dfrac{3}{6}\right):\left(\dfrac{3}{4}-\dfrac{10}{4}\right)\)
\(=\dfrac{7}{6}:\dfrac{-7}{4}\)
\(=\dfrac{7}{6}.\dfrac{4}{-7}\)
\(=-\dfrac{2}{3}\)
b) \(\left(\dfrac{1}{6}+\dfrac{1}{3}\right)^2.\left(1+\dfrac{2}{3}-\dfrac{5}{4}\right)\)
\(=\left(\dfrac{1}{6}+\dfrac{2}{6}\right)^2.\left(\dfrac{12}{12}+\dfrac{8}{12}-\dfrac{15}{12}\right)\)
\(=\left(\dfrac{1}{2}\right)^2.\dfrac{5}{12}\)
\(=\dfrac{1}{4}.\dfrac{5}{12}\)
\(=\dfrac{5}{48}\)
c) \(\dfrac{4^{30}.3^{43}}{2^{57}.27^{15}}\)
\(=\dfrac{4^{30}.27^{40}}{4^{55}.27^{15}}\)
\(=\dfrac{4^{30}.27^{15}.27^{25}}{4^{30}.4^{25}.27^{15}}\)
\(=\dfrac{27^{25}}{4^{25}}\)
a/ \(\left(\dfrac{5}{3}-\dfrac{1}{2}\right):\left(\dfrac{3}{4}-\dfrac{5}{2}\right)\)
= \(\dfrac{7}{6}:\dfrac{-7}{4}\)
= \(\dfrac{-2}{3}\)
b/ \(\left(\dfrac{1}{6}+\dfrac{1}{3}\right)^2.\left(1+\dfrac{2}{3}-\dfrac{5}{4}\right)\)
= \(\dfrac{1}{2}\cdot\dfrac{5}{12}\)
= \(\dfrac{5}{24}\)
c/ \(\dfrac{4^{30}\cdot3^{43}}{2^{57}\cdot27^{15}}\)
= \(\dfrac{\left(2^2\right)^{30}.3^{43}}{2^{57}\cdot\left(3^3\right)^{15}}\)
= \(\dfrac{2^{60}\cdot3^{43}}{2^{57}.3^{45}}\)
= \(\dfrac{2^3}{3^2}\)
= \(\dfrac{8}{9}\)
Tl sai câu c), đính chính thế, đừng ai vô cmt
