Question

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Answer 1

1:

\(A=\dfrac{6.62^2+5,4\cdot3,38+2,22\cdot3,38}{20.1^2-13^2+33.1\cdot12.9}\)

\(=\dfrac{6.62^2+3.38\left(5.4+2.22\right)}{\left(20.1-13\right)\left(20.1+13\right)+33.1\cdot12.9}\)

\(=\dfrac{6.62^2+3.38\cdot7,62}{33.1\left(20.1-13+12.9\right)}\)

\(=\dfrac{69.58}{33.1\cdot20}=\dfrac{3479}{33100}\)

\(B=\dfrac{\left(1,09-0,29\right)\cdot1\dfrac{1}{4}}{18,9-16\dfrac{3}{20}-\dfrac{8}{9}}\)

\(=\dfrac{0.9\cdot1.25}{2.75-\dfrac{8}{9}}=\dfrac{9}{8}:\left(\dfrac{11}{4}-\dfrac{8}{9}\right)\)

\(=\dfrac{9}{8}:\dfrac{99-32}{36}=\dfrac{9}{8}:\dfrac{67}{36}\)

\(=\dfrac{9}{8}\cdot\dfrac{36}{67}=\dfrac{81}{134}\)

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

\(=4\cdot\left(\dfrac{5}{4}\right)^2+25\cdot\left[\dfrac{256}{81}:\dfrac{125}{64}\right]:\left(-\dfrac{8}{27}\right)\)

\(=\dfrac{25}{4}+25\cdot\dfrac{256}{81}\cdot\dfrac{64}{125}\cdot\dfrac{-27}{8}\)

\(=\dfrac{25}{4}+\dfrac{1}{5}\cdot\dfrac{-1}{3}\cdot32\)

\(=\dfrac{25}{4}-\dfrac{32}{15}=\dfrac{247}{60}\)