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Question

Simplify $(9^{4 / 3} \div 27^{2 / 3}) \times 3^{3 / 2}$
$3^{13 / 6}$
$3^{9 / 5}$
$3^{37 / 6}$
None of these

A

3^{9 / 5}

B

3^{37 / 6}

C

3^{13 / 6}

D

None of these

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Solution

Verified by Toppr

The correct option is B $3^{13 / 6}$
$({(3^{2})}^{4 / 3} \div {(3^{3})}^{2 / 3}) \times 3^{3 / 2}$
$= 3^{8 / 3} \div 3^{2} \times 3^{3 / 2}$
$= 3^{8 / 3 - 2 + 3 / 2}$
$= 3^{\frac{16 - 12 + 9}{6}}$
$= 3^{13 / 6}$

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