b)
[tex]\it \left(\dfrac{1}{5}\right)^{-25} \cdot25^{-6}\cdot125^{-4} = \left[\left (\dfrac{1}{5}\right)^{-1} \right]^{25} \cdot(5^2)^{-6} \cdot (5^3)^{-4} =
\\\;\\ \\\;\\
=5^{25}\cdot5^{-12}\cdot5^{-12} = 5^{25-12-12} =5^1=5[/tex]
e)
[tex]\it (10^{-2}-1)(10^{-2}+1)=(10^{-2})^2 -1^2 = 10^{-4} -1= \dfrac{1}{10^4} -1 =
\\\;\\ \\\;\\
=\dfrac{1}{10000}-1=\dfrac{1-10000}{10000} =-\dfrac{9999}{10000}[/tex]
