Simplify: \( \backslash\left(a^{4} b^{5}\right)^{2} \div\left(a^{9} b^{7}\right)^{0} \mid \div a b^{2} \) (3marks)

Let's simplify the expression step by step: 1. Start with \( \left(a^{4} b^{5}\right)^{2} \): \[ \left(a^{4} b^{5}\right)^{2} = a^{4 \cdot 2} b^{5 \cdot 2} = a^{8} b^{10} \] 2. Now simplify \( \left(a^{9} b^{7}\right)^{0} \): \[ \left(a^{9} b^{7}\right)^{0} = 1 \quad \text{(any non-zero expression raised to the power of 0 is 1)} \] 3. So now our expression becomes: \[ \frac{a^{8} b^{10}}{1} \div a b^{2} \] 4. We can rewrite the division: \[ a^{8} b^{10} \div a b^{2} = a^{8} b^{10} \cdot \frac{1}{a b^{2}} \] This is the same as multiplying by the reciprocal: \[ = a^{8} b^{10} \cdot \frac{1}{a} \cdot \frac{1}{b^{2}} = a^{8-1} b^{10-2} = a^{7} b^{8} \] Thus, the simplified expression is: \[ \boxed{a^{7} b^{8}} \]