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

Simplify the expression by following steps: - step0: Solution: \(\frac{\left(3.2^{m}-4.2^{m-2}\right)}{\left(2^{m}-2^{m-1}\right)}\) - step1: Remove the parentheses: \(\frac{3.2^{m}-4.2^{m-2}}{2^{m}-2^{m-1}}\) - step2: Convert the expressions: \(\frac{\left(\frac{16}{5}\right)^{m}-4.2^{m-2}}{2^{m}-2^{m-1}}\) - step3: Convert the expressions: \(\frac{\left(\frac{16}{5}\right)^{m}-\left(\frac{21}{5}\right)^{m-2}}{2^{m}-2^{m-1}}\) - step4: Subtract the terms: \(\frac{\left(\frac{16}{5}\right)^{m}-\left(\frac{21}{5}\right)^{m-2}}{2^{m-1}}\) - step5: Expand the expression: \(\frac{\frac{16^{m}-25\times 21^{m-2}}{5^{m}}}{2^{m-1}}\) - step6: Multiply by the reciprocal: \(\frac{16^{m}-25\times 21^{m-2}}{5^{m}}\times \frac{1}{2^{m-1}}\) - step7: Multiply the terms: \(\frac{16^{m}-25\times 21^{m-2}}{5^{m}\times 2^{m-1}}\) To simplify the expression \[ \frac{3.2^{m}-4.2^{m-2}}{2^{m}-2^{m-1}}, \] we can follow these steps: 1. **Simplify the denominator**: The denominator \(2^{m} - 2^{m-1}\) can be factored as follows: \[ 2^{m} - 2^{m-1} = 2^{m-1}(2 - 1) = 2^{m-1}. \] 2. **Simplify the numerator**: The numerator \(3.2^{m} - 4.2^{m-2}\) can be rewritten by factoring out \(2^{m-2}\): \[ 3.2^{m} - 4.2^{m-2} = 2^{m-2}(3.2^{2} - 4) = 2^{m-2}(3 \cdot 4 - 4) = 2^{m-2}(12 - 4) = 2^{m-2} \cdot 8 = 8 \cdot 2^{m-2}. \] 3. **Combine the results**: Now we can substitute the simplified numerator and denominator back into the expression: \[ \frac{8 \cdot 2^{m-2}}{2^{m-1}}. \] 4. **Further simplification**: This simplifies to: \[ 8 \cdot \frac{2^{m-2}}{2^{m-1}} = 8 \cdot 2^{-1} = \frac{8}{2} = 4. \] Thus, the simplified form of the original expression is \[ 4. \]