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

Aplicando propriedades de potencias

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