Question

Tính

a) (\(\dfrac{3}{7}\)+\(\dfrac{1}{2}\))² b) (\(\dfrac{3}{4}\)-\(\dfrac{5}{6}\))² c) \(\dfrac{5^4.20^4}{25^5.4^5}\) d) (\(\dfrac{-10}{3}\))⁵.(\(\dfrac{-6}{5}\))⁴

Answer 1

a, \(\left(\dfrac{3}{7}+\dfrac{1}{2}\right)^2=\left(\dfrac{3}{7}\right)^2+2.\dfrac{3}{7}.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\)

\(=\dfrac{9}{49}+\dfrac{3}{7}+\dfrac{1}{4}=\dfrac{169}{196}\)

b, \(\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2=\left(\dfrac{3}{4}\right)^2-2.\dfrac{3}{4}.\dfrac{5}{6}+\left(\dfrac{5}{6}\right)^2\)

\(=\dfrac{9}{16}-\dfrac{5}{4}+\dfrac{25}{36}=\dfrac{1}{144}\)

c, \(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.5^4.4^4}{5^{10}.4^5}=\dfrac{1}{5^2.4}=\dfrac{1}{100}\)

d, \(\left(\dfrac{-10}{3}\right)^5.\left(\dfrac{-6}{5}\right)^4=\dfrac{\left(-10\right)^5}{3^5}.\dfrac{6^4}{5^4}\)

\(=\dfrac{5^5.\left(-2\right)^5.2^4.3^4}{3^5.5^4}=\dfrac{-\left(5.2^9\right)}{3}=\dfrac{-2560}{3}\)

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