Answer
(a)$$(\frac{a}{b})^{-n} = \frac{a^{-n}}{b^{-n}} = \frac{\frac{1}{a^n}}{\frac{1}{b^n}} = \frac{1}{a^n}\div\frac{1}{b^n} = \frac{1}{a^n}\times\frac{b^n}{1} = \frac{b^n}{a^n}$$
(b)
$$\frac{a^{-n}}{b^{-m}} = \frac{\frac{1}{a^n}}{\frac{1}{b^m}} = \frac{1}{a^n}\div\frac{1}{b^m} = \frac{1}{a^n}\times\frac{b^m}{1} = \frac{b^m}{a^n}$$
Work Step by Step
(a)
According to the law 6: $(\frac{a}{b})^{-n} = \frac{b^n}{a^n}$
To prove this let's try to simplify left side of this equation
$$(\frac{a}{b})^{-n} = \frac{a^{-n}}{b^{-n}} = \frac{\frac{1}{a^n}}{\frac{1}{b^n}} = \frac{1}{a^n}\div\frac{1}{b^n} = \frac{1}{a^n}\times\frac{b^n}{1} = \frac{b^n}{a^n}$$
(b)
We will follow the same idea this time, simplify left-hand side of the equation and try to make it equal to right-hand side of the equation. According to the law 7, we have: $\frac{a^{-n}}{b^{-m}}=\frac{b^m}{a^n}$
$$\frac{a^{-n}}{b^{-m}} = \frac{\frac{1}{a^n}}{\frac{1}{b^m}} = \frac{1}{a^n}\div\frac{1}{b^m} = \frac{1}{a^n}\times\frac{b^m}{1} = \frac{b^m}{a^n}$$
