Question

Calculati: a) [(-3 pe 2)^4*(-3 pe 2)^5] / (-2 pe 3)^-7

Answer 1

$\frac{( - \frac{3}{2})^{4} * (- \frac{3}{2} )^{5} }{ (- \frac{2}{3} )^{7} } = \\ = \frac{ \frac{3^{4}}{2^{4}} * (- \frac{3^{5}}{2^{5}} ) }{ (- \frac{2^{7}}{3^{7}} )} = \\ =\frac{ \frac{3^{4}}{2^{4}} * \frac{3^{5}}{2^{5}}}{ \frac{2^{7}}{3^{7}}} = \\ =\frac{ \frac{3^{4+5}}{2^{4+5}}}{ \frac{2^{7}}{3^{7}}} = \\ = \frac{ \frac{3^{9}}{2^{9}}}{ \frac{2^{7}}{3^{7}}} = \\ = \frac{3^{9}}{2^{9}}* \frac{3^{7}}{2^{7}} = \\ = \frac{3^{9+7}}{2^{9+7}} = \\ = \frac{3^{16}}{2^{16}}$