СРОЧНО СДЕЛАЙТЕ ПОЖАЛУЙСТА 50балов

Question 1

СРОЧНО СДЕЛАЙТЕ ПОЖАЛУЙСТА
50балов

Question 2

1.
1)
$\frac{15^{2/3} *3^ {7/3} }{5^{-1/3}} = \frac{5^{2/3}*3^{2/3} *3^ {7/3} }{5^{-1/3}} =5^{2/3-(-1/3)}*3^{2/3+7/3}= \\ 5^{2/3+1/3}*3^{9/3}=5^{3/3}*3^{9/3}=5^1*3^3=5*27=135$

2)
$( \frac{4}{5} )^2-( \frac{1}{27})^{1/3}+4*379^0=16/25- 1/3+4*1=48/75-25/75+4= \\ 23/75+4=4 \frac{23}{75}$

3)
$( \sqrt[3]{128}+ \sqrt[3]{ \frac{1}{4} } ): \sqrt[3]{2}= \frac{ \sqrt[3]{128}}{\sqrt[3]{2}}+ \frac{ \sqrt[3]{ \frac{1}{4}}}{\sqrt[3]{2}}= \frac{ \sqrt[3]{64*2}}{\sqrt[3]{2}}+ \frac{ \sqrt[3]{ \frac{1}{4}}}{\sqrt[3]{8*1/4}}= \\ \frac{ \sqrt[3]{64} \sqrt[3]{2}}{\sqrt[3]{2}}+ \frac{ \sqrt[3]{ \frac{1}{4}}}{\sqrt[3]{8}\sqrt[3]{1/4}}=\frac{ \sqrt[3]{64} }{1}+ \frac{1}{\sqrt[3]{8}}= \sqrt[3]{64}+ \frac{\sqrt[3]{8}}{\sqrt[3]{8}*\sqrt[3]{8}}= \\$
$\sqrt[3]{64}+ \frac{\sqrt[3]{8}}{1}= \sqrt[3]{64}+ \sqrt[3]{8}= 4+2=8$

2.
1)
$\sqrt[3]{ \frac{ab^2}{c} }* \sqrt[3]{ \frac{a^5b}{c^2} }= \sqrt[3]{ \frac{ab^2*a^5b}{c*c^2} }= \sqrt[3]{ \frac{a^6b^3}{c^3} }= \frac{a^2b}{c}$

2)
$\frac{a^{-3}*a^{7/3}}{a^{1/3}} = \frac{a^{-3}*a^{7/3-1/3}}{1} =a^{-3}*a^{6/3}=a^{-3}*a^{2}=a^{-1}=1/a$

3.
$\frac{a-9a^{1/2}}{7a^{1/4}+21} = \frac{a^{1/2}(a^{1/2}-9)}{7(a^{1/4}+3)} =\frac{a^{1/2}((a^{1/4})^2-3^2)}{7(a^{1/4}+3)} = \\ =\frac{a^{1/2}(a^{1/4}-3)(a^{1/4}+3)}{7(a^{1/4}+3)} = \frac{a^{1/2}(a^{1/4}-3)}{7} = \frac{a^{1/2+1/4}-3a^{1/2}}{7} = \\ \frac{a^{2/4+1/4}-3a^{1/2}}{7} = \frac{a^{3/4}-3a^{1/2}}{7}$

4.
$\sqrt[5]{(2/9)^3} .... \sqrt[5]{(1/4)^3} \\ \sqrt[5]{(8/36)^3} < \sqrt[5]{(9/36)^3} \\$

5.
(∛a+∛b)²-(∛a-∛b)²=(∛a+∛b-(∛a-∛b))*(∛a+∛b+(∛a-∛b))=
(∛a+∛b-∛a+∛b)*(∛a+∛b+∛a-∛b)=2∛b*2∛a=4∛b∛a