Question

Упростите и вычислите (9a^-5/24/a^1/8a^5/3) при a=24

Answer 1

$left( cfrac{9a^{- frac{5}{24} }}{a^{ frac{1}{8} }a^{ frac{5}{3} }} right)^{ frac{1}{3} }=left( cfrac{9a^{- frac{5}{24} }}{a^{ frac{1}{8} + frac{5}{3} } }} right)^{ frac{1}{3} }=left( cfrac{9a^{- frac{5}{24} }}{a^{ frac{43}{24}} }} right)^{ frac{1}{3} }=left( cfrac{9}{a^{ frac{5}{24} }a^{ frac{43}{24}} }} right)^{ frac{1}{3} }=$


$=left( cfrac{9}{a^{ frac{48}{24} } }} right)^{ frac{1}{3} }=left( cfrac{9}{a^{ 2}} right)^{ frac{1}{3} }= sqrt[3]{ cfrac{9}{a^2} }= cfrac{ sqrt[3]{9} }{sqrt[3]{a^2} } = cfrac{ sqrt[3]{9}*sqrt[3]{a} }{sqrt[3]{a^2}* sqrt[3]{a} } =cfrac{ sqrt[3]{9a} }{a}$

при а=24

$cfrac{ sqrt[3]{9a} }{a}=cfrac{ sqrt[3]{9*24} }{24}=cfrac{ sqrt[3]{216} }{24}= cfrac{6}{24}= cfrac{1}{4}=0.25$