Question

(81/16)^0,75-(2/3)^-1​

Answer 1

Resposta:

           VEJA ABAIXO

Explicação passo a passo:

(81/16)^0,75-(2/3)^-1​

Aplicando convenientes propriedades operacionais de potências e raízes

              $(\frac{81}{16} )^{0,75} - (\frac{2}{3}) ^{-1} \\ \\ =(\frac{81}{16} )^{\frac{3}{4} } - (\frac{3}{2}) \\ \\ =(\frac{81}{16} )^{\frac{2}{4} } .(\frac{81}{16})^{\frac{1}{4} } -(\frac{3}{2}) \\ \\ =(\frac{81}{16})^{\frac{1}{2} } .(\frac{81}{16} )^{\frac{1}{2} } -\frac{3}{2} \\ \\ =\frac{3}{2} .\frac{9}{4} -\frac{3}{2} \\ \\ =\frac{3}{2}.(\frac{9}{4} -1)\\ \\ =\frac{3}{2} .(\frac{9}{4} -\frac{4}{4} )\\ \\ =\frac{3}{2} .\frac{5}{4} \\ \\ =\frac{15}{8}$

Answer 2

Resposta:

$\frac{15}{8}$

Explicação passo-a-passo:

$( \frac{81}{16} ) {}^{0.75} - ( \frac{2}{3} ) {}^{ - 1} =$

$( \frac{81}{16} ) {}^{ \frac{3}{4} } - \frac{3}{2} =$

$\sqrt[4]{( \frac{81}{16} ) {}^{3} } - \frac{3}{4} =$

$\sqrt[4]{( \frac{3 {}^{4} }{2 {}^{4} } ) {}^{3} } = \frac{3}{2} =$

$\sqrt[4]{ \frac{3 {}^{12} }{2 {}^{12} } } - \frac{3}{4} = ( \frac{3}{2} ) {}^{3} - \frac{3}{2} =$

$\frac{27}{8} - \frac{3}{2} =$

$\frac{27 - 12}{8} = \frac{15}{8}$