Question
h) \( \frac{3.2^{m}-4.2^{m-2}}{\left(2^{m}-2^{m-1}\right)} \)
Ask by Crawford Stewart. in South Africa
Mar 06,2025
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Simplify the expression \( \frac{3 \times 2^{m} - 4 \times 2^{m-2}}{2^{m} - 2^{m-1}} \) to \( \frac{16^{m} - 25 \times 21^{m-2}}{5^{m} \times 2^{m-1}} \).
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Mind Expander
To simplify the expression \( \frac{3.2^{m}-4.2^{m-2}}{\left(2^{m}-2^{m-1}\right)} \), we can first simplify the denominator. Notice that: \[ 2^{m} - 2^{m-1} = 2^{m-1}(2 - 1) = 2^{m-1} \] Now, let’s rewrite the numerator: \[ 3.2^{m} - 4.2^{m-2} = 3.2^{m} - 4 \cdot \frac{2^{m}}{2^2} = 3.2^{m} - 2^{m} = 2^{m}(3 - 2) = 2^{m} \] Now, substituting back into the expression yields: \[ \frac{2^{m}}{2^{m-1}} = \frac{2^{m}}{2^{m-1}} = 2^{m - (m-1)} = 2^{1} = 2 \] So, the simplified expression is \( 2 \).
