a)
[tex]8^{-2} =(\frac{1}{8})^{2} = \frac{1}{64}\\\\(-8)^{2} = 64\\\\-8^{-2} =-(\frac{1}{8})^{2} = -\frac{1}{64}\\\\-(-\frac{1}{8})^{2} =-(\frac{1}{64}) = -\frac{1}{64}[/tex]
b)
[tex]4^{3} = 64\\\\(-4)^{-3} =(-\frac{1}{4})^{3} = -\frac{1}{64}\\\\-4^{-3} = -(\frac{1}{4})^{3} = -\frac{1}{64}\\\\-(-\frac{1}{4})^{-3} = -(-\frac{4}{1})^{3} =-(-4)^{3} = -(-64) = 64[/tex]
c)
[tex](\frac{1}{3})^{-4} =3^{4} = 81\\\\(-\frac{1}{3})^{4} = \frac{1}{81}\\\\-(-\frac{1}{3})^{-4} = -(-3)^{4} = -(81) = -81[/tex]
d)
[tex](\sqrt{2})^{-6}= (2^{\frac{1}{2}})^{-6} = 2^{\frac{1}{2}\cdot(-6)} = 2^{-3} = (\frac{1}{2})^{3} = \frac{1}{8}\\\\(-\sqrt{2})^{6} = ((-2)^{\frac{1}{2}})^{6} =(-2)^{3} = -8\\\\-(-\sqrt{2})^{-6} = -(-2^{\frac{1}{2}})^{-6} = -(-2^{-3}) = -(-\frac{1}{3})^{3} = -(-\frac{1}{8}) = \frac{1}{8}[/tex]
