Question

Simplifique o valor da expressão a seguir, utilizando as propriedades de
potências: [(x -2 . y 4 ) -3 ] . [(x 3 ) -7 : (y 2 . x -3 ) 5 ].

Answer 1

    $[(x^{-2}y^{4})^{-3}]\times[(x^{3})^{-7}\div(y^{2}x^{-3})^{5}]=$

$=[(x^{-2}y^{4})^{-3}]\times \frac{(x^{3})^{-7}}{(x^{-3}y^{2})^{5}}=$

$=(x^{-2\times(-3)}y^{4\times(-3)})\times \frac{x^{3\times(-7)}}{x^{-3\times5}y^{2\times5}}=$

$=x^{6}y^{-12}\times \frac{x^{-21}}{x^{-15}y^{10}}=$

$=\frac{(x^{6}y^{-12})\times x^{-21}}{x^{-15}y^{10}}=$

$=\frac{x^{6-21}y^{-12}}{x^{-15}y^{10}}=$

$=\frac{x^{-15}y^{-12}}{x^{-15}y^{10}}=$

$=\frac{y^{-12}}{y^{10}}=$

$=y^{-12-10}=$

$=y^{-22}$