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= (a^-6 / b^-3) . (b^-10 / a^5) : (a^-6 / b^-2)
= a^-6 / b^-3 . b^-10 / a^5 . b^-2 / a^-6
= 1/a^5 . b^-10+(-2)-(-3)
= 1/a^5 . b^-10-2+3
= 1/a^5 . b^-12+3
= 1/a^5 . b^-9
= 1/a^5 . 1/b^9
= 1/(a^5 b^9)