Question

Помогите ришить 2 вариант

Answer 1

$1) sqrt[3]{0,3}* sqrt[3]{-0,09} = sqrt[3]{0,3*(-0,09)} = sqrt[3]{-0,027} =-0,3$
$2) sqrt[4]{54*24}= sqrt[4]{(2*3*3*3)*(2*2*2*3)}= sqrt[4]{2^4*3^4}=2*3=6$
$3) sqrt[3]{-20*25*128}=- sqrt[3]{(2^2*5)*(5*5)*2^7} =- sqrt[3]{2^9*5^3} =$$-2^3*5=-40$
$4) frac{ sqrt[5]{160} *2^{-0,25}}{5^{ frac{1}{5} } sqrt[4]{8} } = frac{sqrt[5]{32*5}*2^{- frac{1}{4} } }{ sqrt[5]{5}* sqrt[4]{2^3} } = frac{sqrt[5]{2^5}* sqrt[5]{5} }{ sqrt[5]{5}* sqrt[4]{2^3} *2^{ frac{1}{4} }} = frac{2}{ sqrt[4]{2^3} sqrt[4]{2}}= frac{2}{ sqrt[4]{2^3*2} } = frac{2}{ sqrt[4]{2^4} } = frac{2}{2}$$=2$
$5) sqrt[3]{27^2} *4 frac{17}{27}*36^{- frac{1}{2} } = sqrt[3]{(3^3)^2} * frac{71}{27} * frac{1}{36^{ frac{1}{2} }} = sqrt[3]{3^6} * frac{71}{27}* frac{1}{ sqrt{36} } = frac{3^2*71*1}{27*6}=$$frac{71}{18}=3 frac{17}{18}$
$6)8^{ frac{1}{3} }:2^{-1}+3^{-2}*324^{ frac{1}{2} }= sqrt[3]{8} *2^1+ frac{ sqrt{324} }{3^2} = sqrt[3]{2^3} *2+ frac{ sqrt{4*81}} {9} =$$2*2+ frac{2*9}{9} =4+2=6$
$7) sqrt[5]{17- sqrt{46} } *sqrt[5]{17+ sqrt{46} } =sqrt[5]{(17- sqrt{46} )(17+ sqrt{46} )} =$$sqrt[5]{17^2-( sqrt{46})^2 } = sqrt[5]{289-46} = sqrt[5]{243} = sqrt[5]{3^5} =3$
$8) frac{27^{-3}*256^4*81^2}{16^7*9^0*45^{-1}} = frac{(2^8)^4*(3^4)^2*45}{27^3*16^7*1} = frac{2^{32}*3^8}{(3^3)^3*(2^4)^7} = frac{2^{32}*3^8}{3^9*2^{28}} = frac{2^{32-28}}{3^{9-8}} = frac{2^4}{3^1} = frac{16}{3}$$=5 frac{1}{3}$