Question

Помогите сделать примеры на фото

Answer 1

#1.

$9^{\frac{3}{2} } + 64^{\frac{1}{3} } = 3^{\frac{3*2}{2} } + 4^{\frac{1 * 3}{3} } = 3^3 + 4 = 27 + 4 = 31$

#2.

$\frac{3}{\sqrt{7} -1} = \frac{3 * (\sqrt{7} +1)}{(\sqrt{7} )^2 - 1^2} = \frac{3 * (\sqrt{7} +1)}{7 - 1} = \frac{\sqrt{7} +1}{3}$

#3.

$(\sqrt[6]{27} + \sqrt[4]{64} )(\sqrt[6]{27} - \sqrt[4]{64}) = (3^{\frac{3}{6}} + 8^{\frac{2}{4} }}) (3^{\frac{3}{6}} + 8^{\frac{2}{4} }}) = (\sqrt{3} + \sqrt{8} )(\sqrt{3} - \sqrt{8} ) = 3 - 8 = -5$

#4.

$\frac{log_8128-log_82}{log_236 - log_2 9} = log_8(\frac{128}{2} ) : log_2 (\frac{36}{9} ) = log_864 : log_24 = 2 : 2 = 1$

#5.

$log_87 - log_76 * log_64 = log_87 - log_76 * \frac{log_7(4)}{log_7(6)} = log_87 - log_7(4) = log_2^3(7) - 2log_7(2) = \frac{1}{3} log_2(7) - 2log_7(2)$