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\(a;\frac{2^{78}+2^{79}+2^{80}}{2^{77}+2^{76}+2^{75}}=\frac{2^{78}\left(1+2+2^2\right)}{2^{75}\left(1+2+2^2\right)}=2^3=8\)
b) \(\frac{5^{56}+5^7}{5^{49}+1}=\frac{5^7\left(5^{49}+1\right)}{5^{49}+1}=5^7\)
a)\(-\dfrac{2}{5}.\dfrac{4}{7}+\dfrac{-3}{5}.\dfrac{2}{7}+\dfrac{-3}{5}\)
=\(-\dfrac{2}{5}.\dfrac{4}{7}+\dfrac{3}{7}.\dfrac{-2}{5}+\dfrac{-3}{5}\)
=\(-\dfrac{2}{5}.\left(\dfrac{4}{7}+\dfrac{3}{7}\right)+\dfrac{-3}{5}\)
=\(\dfrac{-2}{5}.1+\dfrac{-3}{5}\)
=\(-\dfrac{2}{5}+\dfrac{-3}{5}\)
=\(-\dfrac{5}{5}\) = -1
\(\dfrac{5}{9}.\dfrac{14}{17}+\dfrac{1}{17}.\dfrac{5}{9}+\dfrac{2}{9}+\dfrac{5}{12}\)
=\(\dfrac{5}{9}.\left(\dfrac{14}{17}+\dfrac{1}{17}\right)+\dfrac{2}{9}+\dfrac{5}{12}\)
=\(\dfrac{5}{9}.\dfrac{15}{17}+\dfrac{2}{9}+\dfrac{5}{12}\)
=\(\dfrac{25}{51}+\dfrac{2}{9}+\dfrac{5}{12}\)
=\(\dfrac{691}{612}\)
\(1+\left(-2\right)+3+\left(-4\right)+5+...+77+\left(-78\right)+79+\left(-80\right)\)
\(=\left[1+\left(-2\right)\right]+\left[3+\left(-4\right)\right]+\left[5+\left(-6\right)\right]+...+\left[77+\left(-78\right)\right]+\left[79+\left(-80\right)\right]\)
\(=-1+\left(-1\right)+\left(-1\right)+...+\left(-1\right)\)
Từ 1 -> 80 có số số hạng là: (80-1):1+1=80 số hạng
=> Có 80:2=40 số -1
\(=-1\cdot40=-40\)
Đặt: \(A=1+\left(-2\right)+3+\left(-4\right)+...+77+\left(-78\right)+79+\left(-80\right)\)
\(\Rightarrow A=1-2+3-4+...+77-78+79-80\)
\(\Rightarrow A=-1-1-...-1-1\) ( \(40\)cặp)
\(\Rightarrow A=-1\times40=-41\)
a)=\(\frac{-2.4}{5.7}+\frac{-3.2}{5.7}+\frac{-3}{5}\)
=\(\frac{-2.4}{5.7}+\frac{-2.3}{5.7}+\frac{-3}{5}\)
=\(\frac{-2}{5}\left(\frac{4+3}{7}\right)+\frac{-3}{5}\)
=\(\frac{-2}{5}.1+\frac{-3}{5}\)
=-1
b)
\(a.\frac{2^{78}+2^{79}+2^{80}}{2^{77}+2^{76}+2^{75}}=2+2^3+2^5=2+8+32=42\)
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