h) \( \frac{3.2^{m}-4.2^{m-2}}{2^{m}-2^{m-1}} \)

To simplify the expression \( \frac{3.2^{m}-4.2^{m-2}}{2^{m}-2^{m-1}} \), let’s break it down step by step. Firstly, observe that we can factor out \( 2^{m-2} \) from the numerator: \[ 3.2^{m} - 4.2^{m-2} = 2^{m-2}(3 \cdot 2^2 - 4) = 2^{m-2}(12 - 4) = 2^{m-2} \cdot 8 = 8 \cdot 2^{m-2} \] Now, let's look at the denominator: \[ 2^{m} - 2^{m-1} = 2^{m-1}(2 - 1) = 2^{m-1} \cdot 1 = 2^{m-1} \] Now we can substitute these factored forms back into our original expression: \[ \frac{8 \cdot 2^{m-2}}{2^{m-1}} \] We can simplify the fraction by canceling out \( 2^{m-2} \): \[ = 8 \cdot \frac{2^{m-2}}{2^{m-1}} = 8 \cdot \frac{1}{2^{1}} = 8 \cdot \frac{1}{2} = 4 \] Thus, the simplified expression is: \[ \boxed{4} \]