Question

Calcule o valor da expressão:

$\sqrt{ \frac{2,133...}{53 + \frac{1}{3} } } ^{ -3}$

Answer 1

Numerador
X=2,1333..
10x=21,333...
100x=213,333...
100x-10x=213,3333-21,333
90x=192
X=32/15
Denominador
53+1/3=160/3
---------x------x--------
(32/15)/(160/3)
(32*3)/(160*15)
1/25
Raiz de 1/25=1/5
(1/5)^(-3)=5^3=125


espero ter ajudado boa noite!! :)

Answer 2

.
$( \sqrt{ \frac{2,133...}{53+ \frac{1}{3} } } )^{-3}=$

para facilitar vamos calcular separadamente numerador e denomonador

$N=2,1333...=2 + \frac{13-1}{90} =2+ \frac{\not12^2}{\not90_{15}} = \frac{30+2}{15} =\frac{32}{15} \\ \\ \\D= 53+ \frac{1}{3} = \frac{159+1}{3} = \frac{160}{3} \\ \\ N\div D= \\ \frac{32}{15} \div \frac{160}{3} = \frac{\not32}{\not15_3} \times \frac{\not3}{\not160_5} = \frac{1}{25} \\ \\ \\ ( \sqrt{\frac{1}{25} } )^{-3}=( \sqrt{25} )^3= \sqrt{(5^2)^3} = \sqrt{5^6} =5^3=125$