Let's work through the questions step by step from the image you uploaded.

(a) Simplify the following expressions:

(i) $\frac{ab^2c}{a^2b c^{-3}}$

We can simplify this by canceling terms and applying the laws of exponents.

• For $a$: $\frac{a}{a^2} = a^{1-2} = a^{-1} = \frac{1}{a}$
• For $b$: $\frac{b^2}{b} = b^{2-1} = b$
• For $c$: ( \