Question

O valor aproximado de: $\frac{ 16^{-0,75 + \sqrt[5]{0,00243} } }{ \frac{2}{3} +4,333... }$ é:

a) 0,045 b) 0,125 c) 0,315 d) 0,085 e) 0,25

Answer 1

( 16 ^ ( - 3 / 4 ) + 3 / 10 ) / ( 2 / 3 + 13 / 3 )

( ( 2 ^ ( - 12 / 4 ) + ( 3 / 10 )) / ( 15 / 3 )

( ( 2 ^ - 3 + ( 3 / 10 ) ) * 3 / 15

( 1 / 8 + 3 / 10 ) * 3 / 15

( 5 + 12 / 40 ) * 3 / 15

17 / 40 * 3 / 15

51 / 600 ≈ 0,085

Alternativa D )

Answer 2

$\frac{16^{-0.75}+\sqrt[5]{0.00243}}{\frac{2}{3}+4.333...}=\frac{(2^4)^{-0.75}+\sqrt[5]{\frac{243}{100000}}}{\frac{2}{3}+(4+\frac{1}{3})}=\frac{2^{-3}+\sqrt[5]{\frac{3^5}{10^5}}}{5}=\frac{\frac{1}{8}+\frac{3}{10}}{5}=\frac{\frac{5+12}{40}}{5}\\\\\\\boxed{\frac{16^{-0.75}+\sqrt[5]{0.00243}}{\frac{2}{3}+4.333...}=\frac{17}{200}}$

Alternativa d) 0.085