F.3 Maths problem

1.
(2a^-2 + a^-2)^3
= (3a^-2)^3
= 3^3 a^(-2´3)
= 27a^-6
= 27/a^6


2.
(-7/x^-5)^-2 (49x^-8)
= {(-7)^-2 / x[(-5)´(-2)]} (49x^-8)
= [(1/49) / x^10] (49 x^-8)
= [(1/49)´49] x^(-8-10)
= x^-18
= 1/x^18


3.
(2^-2 c^0 d)^-1 / [(cd^-2)^2 (c^-1d)^0]
= (c^-2 d)^-1 / (cd^-2)^2
= {c^[(-2)´(-1)] d^-1} / [c^2 d^(-2´2)]
= (c^2 d^-1) / (c^2 d^-4)
= c^(2-2) d^[-1-(-4)]
= d^3