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0,25 = (0,5)2
\(\dfrac{1}{49}\) = (\(\dfrac{1}{7}\))2
- \(\dfrac{27}{125}\) = (- \(\dfrac{3}{5}\))3
\(\dfrac{81}{16}\) = ( \(\dfrac{9}{4}\))2
\(\dfrac{169}{196}\) = (\(\dfrac{13}{14}\))2
a: \(=7\cdot\dfrac{6}{7}-5+\dfrac{3\sqrt{2}}{2}=1+\dfrac{3}{2}\sqrt{2}\)
b: \(=-\dfrac{8}{7}-\dfrac{3}{5}\cdot\dfrac{5}{8}+\dfrac{1}{2}=\dfrac{-16+7}{14}-\dfrac{3}{8}=\dfrac{-9}{14}-\dfrac{3}{8}\)
\(=\dfrac{-72-42}{112}=\dfrac{-114}{112}=-\dfrac{57}{56}\)
c: \(=20\sqrt{5}-\dfrac{1}{4}\cdot\dfrac{4}{3}+\dfrac{3}{2}=20\sqrt{5}+\dfrac{3}{2}-\dfrac{1}{3}=20\sqrt{5}+\dfrac{7}{6}\)
\(-\dfrac{8}{27}=\left(-\dfrac{2}{3}\right)^3\)
\(\dfrac{81}{625}=\left(\dfrac{3}{5}\right)^4\)
\(\dfrac{25}{49}=\left(\dfrac{5}{7}\right)^2\)
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\(D=49+64+81+...+169\)
\(\Rightarrow D=\frac{\left(169+49\right)\left[\left(169-49\right):15+1\right]}{2}\)
\(\Rightarrow D=\frac{218.9}{2}\)
\(\Rightarrow D=981\)