Question

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Answer 1

$(5\sqrt[3]{4})^3=5^3*(\sqrt[3]{4})^3=125*4=500\\ (-\sqrt[4]{21^4})=-|21|=-21\\ -5\sqrt[5]{7^5}=-5*7=-35\\ \\ \sqrt[4]{\frac{1}{16} }-\sqrt[3]{\frac{64}{125} }=\sqrt[4]{(\frac{1}{2})^4 }-\sqrt[3]{(\frac{4}{5} )^3}=|\frac{1}{2}|-\frac{4}{5}=\frac{1}{2} -\frac{4}{5}=\frac{1*5-4*2}{2*5}=\\ \\ =\frac{5-8}{10}=-\frac{3}{10}=-0,3\\$

$\sqrt[4]{\frac{81}{625} }-\sqrt[3]{\frac{1}{8} }=\sqrt[4]{(\frac{3}{5})^4 } -\sqrt[3]{(\frac{1}{2})^3 } =|\frac{3}{5}| -\frac{1}{2}=\frac{3}{5} -\frac{1}{2}=\frac{3*2-1*5}{5*2}=\\ \\ =\frac{6-5}{10}=\frac{1}{10}=0,1\\ \\ \sqrt[6]{\frac{1}{64} }-\sqrt[4]{\frac{1}{81} }=\sqrt[6]{(\frac{1}{2})^6 }- \sqrt[3]{(\frac{1}{3})^3 }=|\frac{1}{2}|-\frac{1}{3}=\frac{1}{2}-\frac{1}{3}=\frac{3-2}{2*3}=\frac{1}{6}$

$\sqrt[3]{0,027}-\sqrt[5]{-0,00032}=\sqrt[3]{(0,3)^3}+\sqrt[5]{(0,2)^5}=0,3+0,2=0,5\\ (-4\sqrt[4]{7})^4=(-4)^4*(\sqrt[4]{7})^4=256*|7|=256*7=1792\\ \sqrt[5]{0,01024}+\sqrt[3]{-0,027}=\sqrt[5]{(0,4)^5}-\sqrt[3]{(0,3)^3}=0,4-0,3=0,1$

Объяснение: