Question

Efectuar: (9A) + (B/19), SIENDO A Y B RESPECTIVAMENTE:

Answer 1

Respuesta:

109/36

Explicación paso a paso:

Hallando A:

$A=\sqrt{\sqrt[3]{\sqrt{[(\frac{125}{729} )^2]^4} } } \\\\A=\sqrt[3\times 2\times 2]{(\frac{125}{729}) ^ {2\times 4} } \\\\A=\sqrt[12]{(\frac{125}{729}) ^ {8} } \\\\A=(\frac{125}{729}) ^ {\frac{8}{12} } \\\\A=(\frac{125}{729}) ^ {\frac{2}{3} }\\\\A=\sqrt[3]{(\frac{125}{729}) }^2 \\\\A=(\frac{\sqrt[3]{125} }{\sqrt[3]{729} } )^2\\\\A=(\frac{5}{9} )^2\\\\A=\frac{25}{81}$

Hallando B:

$B=(\frac{2}{5} )^{-1}+(\frac{2}{3} )^{-2}\\\\B=\frac{5}{2} +(\frac{3}{2})^2 \\\\B=\frac{5}{2}+\frac{9}{4} \\\\B=\frac{10}{4}+\frac{9}{4} \\\\ B=\frac{10+9}{4} \\\\B=\frac{19}{4}$

Efectuar: (9A)+(B/19)

$(9A)+(\frac{B}{19} )\\\\(9\times \frac{25}{81})+(\frac{\frac{19}{4} }{19} ) \\\\\frac{25}{9} +\frac{19}{19\times 4} \\\\ \frac{25}{9}+\frac{1}{4} \\\\\frac{25\times 4+1\times 9}{36} \\\\\frac{100+9}{36} \\\\\frac{109}{36}$