В геометрической прогрессии {a_n} a_6=-13. Найдите a_4*a_8.

\[a_{6} = - 13 \Longrightarrow a_{6} = b_{1}q^{5};\]

\[a_{4} = b_{1}q^{3}\]

\[a_{8} = b_{1}q^{7}\]

\[a_{4} \cdot a_{8} = b_{1}q^{3} \cdot b_{1}q^{7} =\]

\[= b_{1}^{2} \cdot q^{10} = \left( b_{1}q^{5} \right)^{2} = \left( a_{6} \right)^{2} =\]

\[= ( - 13)^{2} = 169\]

\[Ответ:169.\]