Solve 91-3- 27 1-2-36 - 31-3

9^1/3× 27^1/2/3^1/6× 3^1/3 =(3^2)^1/3×(3^3)^1/2/(3)^1/6× (3)^1/3 =3^2/3× 3^3/2/(3)^1/6× (3)^1/3 =(3)^2/3+3/2/(3)^1/6+1/3=(3)^13/6/(3)^3/6=(3)^13/6 3/6 =3^10/ ...

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Byju's Answer

Standard XII

Mathematics

Greatest Integer Function

Solve 91/3× 2...

Question

Solve $\frac{9^{\frac{1}{3}} \times 27^{\frac{1}{2}}}{3^{\frac{1}{6}} \times 3^{\frac{1}{3}}}$

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Solution

$\frac{9^{\frac{1}{3}} \times 27^{\frac{1}{2}}}{3^{\frac{1}{6}} \times 3^{\frac{1}{3}}} = \frac{(3^{2})^{\frac{1}{3}} \times (3^{3})^{\frac{1}{2}}}{(3)^{\frac{1}{6}} \times (3)^{\frac{1}{3}}} = \frac{3^{\frac{2}{3}} \times 3^{\frac{3}{2}}}{(3)^{\frac{1}{6}} \times (3)^{\frac{1}{3}}}$
$= \frac{(3)^{\frac{2}{3}} + \frac{3}{2}}{(3)^{\frac{1}{6}} + \frac{1}{3}} = \frac{(3)^{\frac{13}{6}}}{(3)^{\frac{3}{6}}} = (3)^{\frac{13}{6} - \frac{3}{6}} = 3^{\frac{10}{6}} = 3^{\frac{5}{3}}$

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Solve 913×2712316×313

913×2712316×313=(32)13×(33)12(3)16×(3)13=323×332(3)16×(3)13 =(3)23+32(3)16+13=(3)136(3)36=(3)136−36=3106=353

Solve $\frac{9^{\frac{1}{3}} \times 27^{\frac{1}{2}}}{3^{\frac{1}{6}} \times 3^{\frac{1}{3}}}$