$a^{-7} * a^{10} = a^{-7 + 10} = a^3$

$a^{-9} * a^5 = a^{-9 + 5} = a^{-4}$

$a^{17} * a^{-4} * a^{-11} = a^{17 - 4 - 11} = a^{2}$

$a^{-2} : a^3 = a^{-2 - 3} = a^{-5}$

$a^{12} : a^{-4} = a^{12 - (-4)} = a^{12 + 4} = a^{16}$

$a^{-7} : a^{-11} = a^{-7 - (-11)} = a^{-7 + 11} = a^4$

$a^{-12} : a^{-10} * a^4 = a^{-12 - (-10) + 4} = a^{-12 + 10 + 4} = a^{2}$

$(a^3)^{-5} = a^{3 * (-5)} = a^{-15}$

$(a^{-12})^{-2} = a^{-12 * (-2)} = a^{24}$

$(a^{-3})^4 : (a^{-2})^5 : (a^{-1})^{-7} = a^{-3 * 4} : a^{-2 * 5} : a^{-1 * (-7)} = a^{-12} : a^{-10} : a^{7} = a^{-12 - (-10) - 7} = a^{-12 + 10 - 7} = a^{-9}$

$(m^{-3}n^4p^7)^{-4} = m^{-3 * (-4)}n^{4 * (-4)}p^{7 * (-4)} = m^{12}n^{-16}p^{-28}$

$(a^{-1}b^{-2})^{-3} = a^{-1 * (-3)}b^{-2 * (-3)} = a^3b^6$

$(x^3y^{-4})^5 * (x^{-2}y^{-3})^3 = x^{3 * 5}y^{-4 * 5} * x^{-2 * 3}y^{-3 * 3} = x^{15}y^{-20} * x^{-6}y^{-9} = x^{15 - 6}y^{-20 - 9} = x^{9}y^{-29}$

$(\frac{a^{11}b^{-7}}{c^{-3}d^4})^{-3} = \frac{a^{11 * (-3)}b^{-7 * (-3)}}{c^{-3 * (-3)}d^{4 * (-3)}} = \frac{a^{-33}b^{21}}{c^{9}d^{-12}} = a^{-33}b^{21}c^{-9}d^{12}$

$(\frac{a^{-7}}{b^5})^{-3} * (\frac{a^{4}}{b^{-7}})^{-5} = \frac{a^{-7 * (-3)}}{b^{5 * (-3)}} * \frac{a^{4 * (-5)}}{b^{-7 * (-5)}} = \frac{a^{21}}{b^{-15}} * \frac{a^{-20}}{b^{35}} = \frac{a^{21 - 20}}{b^{-15 + 35}} = \frac{a}{b^{20}} = ab^{-20}$