Question

Решите самостоятельную работу

Answer 1

Объяснение:

$1) \sqrt[4]{(-3)^2 * 2} * \sqrt[4]{8 * 9} = \sqrt[4]{(-3)^2 * 2 * 8 * 9} = \sqrt[4]{9 * 2 * 8 * 9} = \sqrt[4]{9^2 * 16} = \sqrt[4]{3^4 * 2^4} = 3*2 = 6$

$2) \sqrt[3]{-64\sqrt{a^{18}}} = \sqrt[3]{-64|a|^9} = \sqrt[3]{-2^6|a|^9} = -\sqrt[3]{2^6|a|^9} = -4|a|^3 = 4a^3$

$3) $ \left(b^\frac{5}{6}\right)^3 * \sqrt[4]{b^3} = b^\frac{5}{2} * b^\frac{3}{4} = b^{\frac{10}{4} + \frac{3}{4}} = b^\frac{13}{4} = \sqrt[4]{b^{13}} = |b|^3\sqrt[4]{b}$$

$4)\\a) \ 6*8^{-\frac{1}{3}} = \frac{6}{8^\frac{1}{3}} = \frac{6}{\sqrt[3]{8}} = \frac{6}{2} = 3\\b) \ $\left(\frac{36^3}{125^2}\right)^\frac{1}{6} = \left(\frac{6^6}{5^6}\right)^\frac{1}{6} = \frac{6}{5} =1.2$\\c) $\left(0.216^\frac{8}{27}\right)^\frac{9}{4} = 0.216^{\frac{8}{27}*\frac{9}{4}} = 0.216^\frac{2}{3} = (0.6^3)^\frac{2}{3} = 0.36$$

$5) \sqrt{43 - 30\sqrt{2}} * \sqrt{43 * 30\sqrt{2}} = \sqrt{(43 - 30\sqrt{2})(43 * 30\sqrt{2})} = \sqrt{43^2 - 30^2*(\sqrt{2})^2} = \sqrt{1849 - 1800} = \sqrt{49} = 7$

$6) 16^{-\frac{5}{4}} - (0.01)^{-\frac{1}{2}} + (7^0)^3 - 16 * 2^{-5} * 64^{-\frac{2}{3}} = \frac{1}{16^{\frac{5}{4}}} - 100^{\frac{1}{2}} + 1 - \frac{16}{32} * \frac{1}{64^{\frac{2}{3}}} =\frac{1}{32} - 10 + 1 - \frac{1}{2} * \frac{1}{16} = \frac{1}{32} - 9 -\frac{1}{32} = -9$