Question

Qual o valor da expressão $\frac{ (4^{ \frac{3}{2} }- 8^{ \frac{2}{3} })^{ \frac{3}{2} } }{ [2^{0} + 3^{-1} . 6 - ( \frac{3}{4}) ^{0}]^{2} }$?

Answer 1

√(√4³ - ∛8²)³ / (1 + 1/3 . 6 - 1)² =
√(8 - 4)³ / (0 + 6/3)² =
√4 / 2² = 
2/4 = 1/2

Answer 2

Aplicando propriedades de potencias

      $\frac{( 4^{ \frac{3}{2} }- 8^{ ^{ \frac{2}{3}} })^{ \frac{3}{2} } }{[2^0+ 3^{-1} .6- (\frac{3}{4})^0]^2 } \\ \\ = \frac{[(2^2) ^{ \frac{3}{2}}-(2^3) ^{ \frac{2}{3} }] ^{ \frac{3}{2} } }{[1+ \frac{1}{3}.6-1]^2 } \\ \\ = \frac{[2^3-2^2] ^{ \frac{3}{2} } }{[1+2-1]^2} \\ \\ = \frac{[8-4]^{ \frac{3}{2} } }{2^2} \\ \\ = \frac{(2^2) ^{ \frac{3}{2} } }{2^2} \\ \\ = 2^{3-2} \\ \\ =2$