Question

prove m-n=2 (question in the picture above=

Answer 1

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$\frac{ {9}^{n + 1} \times { {3}^{ (- \frac{n}{2}) } }^{ - 2} - {27}^{n} }{( {3}^{m} \times 2)^{3} } = \frac{1}{729} \\ or. \: \frac{ { {3}^{2} }^{(n + 1)} \times {3}^{n} - {3}^{3n} }{ {3}^{3m} \times 2^{3} } = {3}^{ - 6} \\ or. \: {3}^{2n + 2 + n} - {3}^{3n} = 8 \times {3}^{3m} \times {3}^{ - 6} \\ or. \: {3}^{3n} ( {3}^{2} - 1) = 8 \times {3}^{3m - 6} \\ or. \: 8 \times {3}^{3n} = 8 \times {3}^{3m - 6 } \\ \\ so..3n = 3m - 6 \\ or. \: 3m - 3n = 6 \\ or. \: m - n = 2....proved..$
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