\(\left(3-\dfrac{1}{2}\right)^3-\dfrac{5^4}{25}+\left[\left(\dfrac{1}{2}\right)^2\right]^3\)
\(=\left(\dfrac{5}{2}\right)^3-\dfrac{5^4}{5^2}+\left[\left(\dfrac{1}{2}\right)^2\right]^3\)
\(=\left(\dfrac{5}{2}\right)^3+\left[\left(\dfrac{1}{2}\right)^2\right]^3-5\)
\(=\left(\dfrac{5}{2}+\dfrac{1}{2}\right)\left[\left(\dfrac{5}{2}\right)^2-\dfrac{5}{2}.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\right]-5\)
\(=3\left[\dfrac{25}{4}+\dfrac{1}{4}-\dfrac{5}{4}\right]-5\)
\(=3.\dfrac{21}{4}-5\)
\(=\dfrac{63}{4}-5=\dfrac{43}{4}\)
Đính chính \(\dfrac{5^4}{5^2}=25\)
\(...=\dfrac{63}{4}-25=-\dfrac{37}{4}\)
(3 - 1/2)³ - 5⁴/25 + [(1/2)²]³
= (5/2)³ - 25 + (1/2)⁶
= 125/8 - 25 + 1/64
= 1000/64 - 1600/64 + 1/64
= -599/64
