Bài 1 :
a) \(27^4:9^3=\left(3^{^3}\right)^4:\left(3^2\right)^3=3^{12}:3^6=3^6\)
b) \(\dfrac{6^2\cdot3^3}{12^2}=\dfrac{3^3}{4}=\dfrac{27}{4}\)
c) \(\dfrac{12^3\cdot18^2}{24^2}=\dfrac{12^3\cdot18^2}{12^2\cdot2^2}=12\cdot9^2=12\cdot81=972\)
Bài 2 :
a) \(4\cdot\left(-\dfrac{1}{2}\right)+\dfrac{1}{2}=\left(-\dfrac{4}{2}\right)+\dfrac{1}{2}=-\dfrac{3}{2}\)
b) \(\left(\dfrac{3}{5}-\dfrac{3}{4}\right)\cdot\left(\dfrac{1}{3}-\dfrac{1}{5}\right)^2\)
\(=\left(\dfrac{12}{20}-\dfrac{15}{20}\right)\cdot\left(\dfrac{5}{15}-\dfrac{3}{15}\right)^2\)
\(=\left(-\dfrac{3}{20}\right)\cdot\left(\dfrac{2}{15}\right)^2\)
\(=\left(-\dfrac{3}{20}\right)\cdot\dfrac{4}{225}=-\dfrac{1}{375}\)
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