Question

the value of (6^-1×7^2/6^2×7^-2)^7/2×(6^-2×7^3/6^3×7^-5)^-5/2 is

Answer 1

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$= > \bf \: {( \frac{ {6}^{ - 1} {7}^{2} }{ {6}^{2} {7}^{ - 4} } )}^{ \frac{7}{2} } \times {( \frac{ {6}^{ - 2} {7}^{3} }{ {6}^{3} {7}^{ - 5} } )}^{ - \frac{5}{2} } \\ \\ = {( {6}^{ - 3} {7 }^{ 6} )}^{ \frac{7}{ 2} } \times {( {6}^{ - 5} {7}^{8} )}^{ - \frac{5}{2} } \\ \\ = {6}^{ - 3 \times \frac{7}{2} } \times {7}^{6 \times \frac{7}{2} } \times {6}^{ - 5 \times - \frac{5}{2} } \times {7}^{8 \times \frac{ - 5}{2} } \\ \\ = {6}^{ - \frac{21}{2} } \times {7}^{21} \times {6}^{ \frac{25}{2} } \times {7}^{ - 20} \\ \\ = {6}^{ \frac{25}{2} - \frac{21}{2} } \times {7}^{21 - 20} \\ \\ = {6}^{ \frac{4}{2} } \times 7 = {6}^{2} \times 7 \\ \\ = \bf \underline{ \: 252 \: }$
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