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Ta có: \(\left|97\dfrac{2}{3}-125\dfrac{3}{5}\right|+97\dfrac{2}{5}-125\dfrac{1}{3}\)
\(=\left|97+\dfrac{2}{3}-125-\dfrac{3}{5}\right|+97+\dfrac{2}{5}-125-\dfrac{1}{3}\)
\(=\left|-28+\dfrac{1}{15}\right|-28+\dfrac{1}{15}\)
\(=\left|\dfrac{1}{15}-28\right|-28+\dfrac{1}{15}\)
\(=28-\dfrac{1}{15}-28+\dfrac{1}{15}\)
\(=0\)
\(\frac{\left(5^4-5^3\right)}{125^4}-\frac{64}{125}\)
\(=\frac{\left(625-125\right)}{500}-\frac{64}{125}\)
\(=\frac{500}{500}-\frac{64}{125}\)
\(=0-0,51\)
\(=-0,51\)
Ta có: \(\left|97\dfrac{2}{3}-123\dfrac{3}{5}+97\dfrac{2}{5}-125\dfrac{1}{3}\right|\)
\(=\left|97\left(\dfrac{2}{3}+\dfrac{2}{5}\right)-125\cdot\left(\dfrac{3}{5}+\dfrac{1}{3}\right)\right|\)
\(=\left|194\cdot\dfrac{8}{15}-125\cdot\dfrac{14}{15}\right|\)
\(=\left|\dfrac{-66}{5}\right|=\dfrac{66}{5}\)
Ta có:
\(\begin{array}{l}125 = 5.5.5 = {5^3}\\3125 = 5.5.5.5.5 = {5^5}\end{array}\)