Question

Tính \(P=\dfrac{1}{0,25}.\left(1\dfrac{1}{4}\right)^2+25.\left[\dfrac{1}{\left(\dfrac{4}{3}\right)^2}:\left(\dfrac{5}{4}\right)^3\right]:\dfrac{1}{\left(-\dfrac{2}{3}\right)^3}\)

Answer 1

Ta lần lượt có:

\(\dfrac{1}{0,25}=\dfrac{100}{25}=4;\) \(\left(1\dfrac{1}{4}\right)^2=\left(\dfrac{5}{4}\right)^2=\dfrac{25}{16};\)

\(\dfrac{1}{\left(\dfrac{4}{3}\right)^2}=\dfrac{1}{\dfrac{16}{9}}=\dfrac{9}{16};\) \(\left(\dfrac{5}{4}\right)^3=\dfrac{125}{64}\) và \(\dfrac{1}{\left(-\dfrac{2}{3}\right)^3}=\dfrac{1}{-\dfrac{8}{27}}=-\dfrac{27}{8}\)

Vậy \(P=4.\dfrac{25}{16}+25.\left[\dfrac{9}{16}:\dfrac{125}{64}\right]:\left(-\dfrac{27}{8}\right)\)

\(=\dfrac{25}{4}-25.\dfrac{9}{16}.\dfrac{64}{125}.\dfrac{8}{27}\)

\(=\dfrac{25}{4}-\dfrac{32}{15}\)

\(=\dfrac{375-128}{60}=\dfrac{247}{60}\)

Answer 2

P=4.(25/16)+25.(9/16:25/16):(-27/8)

=25/4 +25.(9/25):(-27/8)

=25/4 +9:(-27/8)

=25/4 +(-8/3)

=43/12