Question

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Answer 1

Answer:

$\dfrac{ {2}^{5} \times 7 }{ {3}^{4} }$

Step-by-step explanation:

Solution:

${ (\frac{16}{81}) }^{ \frac{3}{4} } \times { (\frac{49}{9}) }^{ \frac{3}{2} } \div {( \frac{343}{216} )}^{ \frac{2}{3} } \\ \\ \sqrt[4] { {(\frac{16}{81} )}^{3} } \times \sqrt[2]{ { (\frac{49}{9} )}^{3} } \div \sqrt[3] { {(\frac{343}{216} )}^{2} } \\ \\ { (\frac{2}{3} )}^{3} \times { (\frac{7}{3}) }^{3} \div { (\frac{7}{6}) }^{2} \\ \\ \frac{ {2}^{3} }{ {3}^{3} } \times \frac{ {7}^{3} }{ {3}^{3} } \times \frac{ {6}^{2} }{ {7}^{2} } \\ \\ { {2}^{3} } \times \frac{ {7}^{(3 - 2)} }{ {3}^{(3 + 3)} } \times { {(2 \times 3)}^{2} } \\ \\ 2 {}^{3} \times \frac{7}{ {3}^{6} } \times 2 {}^{2} \times {3}^{2} \\ \\ {2}^{(3 + 2)} \times \frac{7}{ {3}^{(6 - 2)} } \\ \\ \frac{ {2}^{5} \times 7} { { 3}^{4} }$

Using laws of Indices

${a}^{x} \times {a}^{2} = {a}^{x + 2} \\ \\ {x}^{5} \times \frac{1}{ {x}^{8} } = \frac{1}{ {x}^{(8 - 5)} } \\ \\ {x}^{ \frac{1}{5} } = \sqrt[5]{x}$

Answer 2

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