\[\boxed{\mathbf{438}.}\]
\[1)\ \sqrt[15]{- 1} = \sqrt[15]{( - 1)^{15}} = - 1;\]
\[2)\ \sqrt[5]{- 1024} = \sqrt[5]{( - 4)^{5}} = - 4;\]
\[3)\ \sqrt[7]{- 8^{7}} = - \sqrt[7]{8^{7}} = - 8.\]