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.

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