Question

va rog dau 100 de puncte​

Answer 1

1)

$\bigg( \dfrac{3}{7}\bigg)^{8} \cdot \bigg( \dfrac{3}{7}\bigg)^{13} = \bigg( \dfrac{3}{7}\bigg)^{8 + 13} =\bigg( \dfrac{3}{7}\bigg)^{21}$

$\dfrac{ {12}^{5} }{ {14}^{5} } \cdot \bigg( \dfrac{6}{7} \bigg)^{7} = \bigg( \dfrac{12 ^{(2} }{14} \bigg)^{5} \cdot \bigg( \dfrac{6}{7} \bigg)^{7} = \bigg( \dfrac{6}{7} \bigg)^{5} \cdot \bigg( \dfrac{6}{7} \bigg)^{7} = \bigg( \dfrac{6}{7} \bigg)^{5 + 7} = \bigg( \dfrac{6}{7} \bigg)^{12}$

$\dfrac{1}{32} \cdot \bigg( \dfrac{1}{2} \bigg)^{23} = \dfrac{{1}^{5}}{ {2}^{5} } \cdot \bigg( \dfrac{1}{2} \bigg)^{23} = \bigg( \dfrac{1}{2} \bigg)^{5} \cdot \bigg( \dfrac{1}{2} \bigg)^{23} = \bigg( \dfrac{1}{2} \bigg)^{5 + 23} = \bigg( \dfrac{1}{2} \bigg)^{28}$

2)

$\bigg( \dfrac{3}{5}\bigg)^{14} : \bigg( \dfrac{3}{5}\bigg)^{9} = \bigg( \dfrac{3}{5}\bigg)^{14 - 9} =\bigg( \dfrac{3}{5}\bigg)^{5}$

$\bigg( \dfrac{5}{6} \bigg)^{7} : \dfrac{ {10}^{5} }{ {12}^{5} } = \bigg( \dfrac{5}{6} \bigg)^{7} : \bigg( \dfrac{10 ^{(2} }{12} \bigg)^{5} = \bigg( \dfrac{5}{6} \bigg)^{7} : \bigg( \dfrac{5}{6} \bigg)^{5} = \bigg( \dfrac{5}{6} \bigg)^{7 - 5} = \bigg( \dfrac{5}{6} \bigg)^{2}$

$\bigg( \dfrac{1}{7} \bigg)^{8} : \dfrac{1}{343} = \bigg( \dfrac{1}{7} \bigg)^{8} :\dfrac{{1}^{3}}{ {7}^{3} } = \bigg( \dfrac{1}{7} \bigg)^{8} :\bigg( \dfrac{1}{7} \bigg)^{3} = \bigg( \dfrac{1}{7} \bigg)^{8 - 3} = \bigg( \dfrac{1}{7} \bigg)^{5}$

3) adevărată

$\dfrac{8^{10}}{32^{6}} = \dfrac{( {2}^{3} )^{10}}{( {2}^{5} )^{6}} = \dfrac{{2}^{3 \times 10}}{{2}^{5 \times 6}} = \dfrac{{2}^{30}}{{2}^{30}} = 1$