Question

simplify the above question​

Answer 1

$\sf\frac{ ({64)}^{ \frac{ - 1}{6}} \times {(216)}^{ \frac{- 1}{3} } \times {(81)}^{ \frac{1}{4} } }{ {(512)}^{ \frac{ - 1}{3} } \times {(16)}^{ \frac{1}{4} } \times {(9)}^{ \frac{ - 1}{2} } } \\ \\ \sf =\frac{ { {(2)}^{6 \times } }^{( \frac{ - 1}{6}) } \times { ( {6})}^{ 3 \times( \frac{ - 1}{3}) } \times ({3})^{4 \times \frac{1}{4} } }{ {(8)}^{3 \times( \frac{ - 1}{3} )} \times {(2)}^{4 \times \frac{1}{4} } \times {(3)}^{2 \times ( \frac{ - 1}{2}) } } \\ \\ = \sf \frac{8 \times 3 \times 3}{2 \times 6 \times 2} \\ \\ \sf = \frac{4 \times 3}{2 \times 2} \\ \\ \red{= \sf 3}$

NOTE : When the power will be negative the number will reciprocal.

During solving this question keep in mind that ;

• 2^6 = 64

• 6^3 = 216

• 3^4 = 81

• 8^3 = 512

• 2^4 = 16

• 3^2 = 9

I HOPE IT HELPS.

Answer 2

Answer:

$\frac{ {(64)}^{ \frac{( - 1)}{6} } \times {(216)}^{ \frac{( - 1)}{3} } \times {(81)}^{ \frac{1}{4} } }{ {(512)}^{ \frac{( - 1)}{3} } \times {(16)}^{ \frac{1}{4} } \times {(9)}^{ \frac{ (- 1)}{2} } } = 3$

Step-by-step explanation:

$\frac{ {(64)}^{ \frac{( - 1)}{6} } \times {(216)}^{ \frac{( - 1)}{3} } \times {(81)}^{ \frac{1}{4} } }{ {(512)}^{ \frac{( - 1)}{3} } \times {(16)}^{ \frac{1}{4} } \times {(9)}^{ \frac{ (- 1)}{2} } } \\ = \frac{ { (\frac{1}{64} )}^{ \frac{1}{6} } \times { (\frac{1}{216}) }^{ \frac{1}{3} } \times {(81)}^{ \frac{1}{4} } }{ { (\frac{1}{512} )}^{ \frac{1}{3} } \times {(16)}^{ \frac{1}{4} } \times { (\frac{1}{9}) }^{ \frac{1}{2} } } \\ = \frac{ { {( \frac{1}{2} }^{6}) }^{ \frac{1}{6} } \times { { (\frac{1}{6} }^{3}) }^{ \frac{1}{3} } \times { {(3}^{4} )}^{ \frac{1}{4} } }{ { { (\frac{1}{8} }^{3}) }^{ \frac{1}{3} } \times { ({2}^{4} )}^{ \frac{1}{4} } \times { { (\frac{1}{3} }^{2} )}^{ \frac{1}{2} } } \\ = \frac{ { (\frac{1}{2} )}^{6 \times \frac{1}{6} } \times { (\frac{1}{6}) }^{3 \times \frac{1}{3} } \times {(3)}^{4 \times \frac{1}{4} } }{ {( \frac{1}{8}) }^{3 \times \frac{1}{3} } \times {(2)}^{4 \times \frac{1}{4} } \times { (\frac{1}{3}) }^{2 \times \frac{1}{2} } } \\ = \frac{ \frac{1}{2} \times \frac{1}{6} \times 3}{ \frac{1}{8} \times 2 \times \frac{1}{3} } \\ = \frac{ \frac{1}{2} \times \frac{1}{2} }{ \frac{1}{4} \times \frac{1}{3} } \\ = \frac{ \frac{1}{4} }{ \frac{1}{12} } \\ = \frac{1}{4} \div \frac{1}{12} \\ = \frac{1}{4} \times 12 \\ = 3$