simplify 9^ 1/3 x 27^1/2 divided by 3^1/6 x 3^-2/3

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Solution

Dear student
$\frac{9^{\frac{1}{3}} \times 27^{\frac{1}{2}}}{3^{\frac{1}{6}} \times 3^{\frac{- 2}{3}}} = \frac{{(3^{2})}^{\frac{1}{3}} \times {(3^{3})}^{\frac{1}{2}}}{3^{\frac{1}{6}} \times 3^{\frac{- 2}{3}}} = 3^{\frac{2}{3} + \frac{3}{2} - \frac{1}{6} - (\frac{- 2}{3})} [S i n c e a^{m} \times a^{n} = a^{m + n} a n d \frac{a^{m}}{a^{n}} = a^{m - n}] = 3^{\frac{4 + 9 - 1 + 4}{6}} = 3^{\frac{16}{6}} = 3^{\frac{8}{3}}$
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simplify 9^ 1/3 x 27^1/2 divided by 3^1/6 x 3^-2/3

Dear student 913×2712316×3-23=3213×3312316×3-23=323+32-16--23 Since am×an=am+n and aman=am-n=34+9-1+46=3166=383 Regards