Question

(81)^3/4×(216)^-2/3×(125)^1/3 by (64)^1/6×(243)^-2/5×(343)^1/3

Answer 1

I hope this would help

Answer 2

$\frac{ {(81)}^{ \frac{3}{4} } \times {(216)}^{ \frac{ - 2}{3} } \times {(125)}^{ \frac{1}{3} } }{ {(64)}^{ \frac{1}{6} } \times {(243)}^{ \frac{ - 2}{5} } \times {(343)}^{ \frac{1}{3} } } \\ \\ \\ = \frac{ {( {3}^{4} )}^{ \frac{3}{4} } \times {( {6}^{3} )}^{ \frac{ - 2}{3} } \times { ({5}^{3}) }^{ \frac{1}{3} } }{ { ({2}^{6}) }^{ \frac{1}{6} } \times { {(3}^{5} )}^{ \frac{ - 2}{5} } \times { ({7}^{3}) }^{ \frac{1}{3} } } \\ \\ \\ = \frac{ {(3)}^{4 \times \frac{3}{4} } \times {(6)}^{3 \times \frac{ - 2}{3} } \times {(5)}^{3 \times \frac{1}{3} } }{ {(2)}^{6 \times \frac{1}{6} } \times {(3)}^{5 \times \frac{ - 2}{5} } \times {(7)}^{3 \times \frac{1}{3} } } \\ \\ \\ = \frac{ {(3)}^{3} \times {(6)}^{ - 2} \times {(5)}^{1} }{ {(2)}^{1} \times {(3)}^{ - 2} \times {(7)}^{1} } \\ \\ \\ = \frac{ {(3)}^{3} \times {(3)}^{2} \times {(5)}^{1} }{ {(2)}^{1} \times {(6)}^{2} \times {(7)}^{1} } \\ \\ \\ = \frac{ {(3)}^{3 + 2} \times {(5)}^{1} }{ {(2)}^{1} \times {(2 \times 3)}^{2} \times {(7)}^{1} } \\ \\ \\ = \frac{ {(3)}^{5} \times {(5)}^{1} }{ {(2)}^{1} \times {(2)}^{2} \times {(3)}^{2} \times {(7)}^{1} } \\ \\ \\ = \frac{ {(3)}^{3 - 2} \times {(5)}^{1} }{ {(2)}^{1 + 2} \times {(7)}^{1} } \\ \\ \\ = \frac{ {(3)}^{3} \times {(5)}^{1} }{ {(2)}^{3} \times {(7)}^{1} } \\ \\ \\ = \frac{27 \times 5}{8 \times 7} \\ \\ \\ = \frac{135}{56}$