Question

СРОЧНО СДЕЛАЙТЕ ПОЖАЛУЙСТА
50балов

Answer 1

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