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Ответ:
Решение:
- 1) \(\begin{align*}\) \(\frac{15^{3} \cdot 3^{3}}{5^{3}}\) \(\cdot\) \(\left\)\(\frac{2}{5}\right\)^{-2} &= \(\frac\){\(3 \cdot 5\)^{3} \(\cdot\) 3^{3}}{5^{3}} \(\cdot\) \(\left\)\(\frac{5}{2}\right\)^{2} \\ &= \(\frac{3^{3} \cdot 5^{3} \cdot 3^{3}}{5^{3}}\) \(\cdot\) \(\frac{5^{2}}{2^{2}}\) \\ &= 3^{6} \(\cdot\) \(\frac{25}{4}\) \\ &= 729 \(\cdot\) \(\frac{25}{4}\) &= \(\frac{18225}{4}\) = 4556.25 \(\end{align*}\)
- 2) \(\begin{align*}\) \(\left\)\(\frac{4}{5}\right\)^{-2} - \(\left\)\(\frac{1}{27}\right\)^{\(\frac{1}{3}\)} + 4 \(\cdot\) 379^0 &= \(\left\)\(\frac{5}{4}\right\)^{2} - \(\frac{1}{3}\) + 4 \(\cdot\) 1 \\ &= \(\frac{25}{16}\) - \(\frac{1}{3}\) + 4 \\ &= \(\frac{25 \cdot 3 - 1 \cdot 16 + 4 \cdot 16 \cdot 3}{48}\) \\ &= \(\frac{75 - 16 + 192}{48}\) \\ &= \(\frac{251}{48}\) \(\end{align*}\)
- 3) \(\begin{align*}\) \(\left\)\(\sqrt[3]{128} + \sqrt[3]{\frac{1}{4}}\right\) : \(\sqrt[3]{\frac{1}{4}}\) &= \(\left\)\(\sqrt[3]{128} : \sqrt[3]{\frac{1}{4}}\right\) + \(\left\)\(\sqrt[3]{\frac{1}{4}} : \sqrt[3]{\frac{1}{4}}\right\) \\ &= \(\sqrt[3]{\frac{128}{\frac{1}{4}}}\) + 1 \\ &= \(\sqrt[3]{128 \cdot 4}\) + 1 \\ &= \(\sqrt[3]{512}\) + 1 \\ &= 8 + 1 = 9 \(\end{align*}\)
Ответ: 1) 4556.25; 2) \(\frac{251}{48}\); 3) 9.
