Simplify- 9 1-3- 271-2-31-6- 3-2-3

The correct option is B 3^2 9^1/3× 27^1/2/3^1/6× 3^ 2/3 = 9^1/3× 3^2/3/3^1/6× 27^1/2 = (3^2)^1/3× 3^2/3/3^1/6× (3^3)^1/2 = 3^2/3 + 2/3/3^1/6 + 3/2 = 3^4/3/3^ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Laws of Exponents for Real Numbers

Simplify: 9 1...

Question

Simplify: $\frac{9^{\frac{1}{3} \times 27^{\frac{1}{2}}}}{3^{\frac{1}{6}} \times 3^{- \frac{2}{3}}}$

$\sqrt{3}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$(3)^{- \frac{1}{3}}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$3^{2}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$3^{\frac{1}{2}}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$3^{2}$

$\frac{9^{\frac{1}{3} \times 27^{\frac{1}{2}}}}{3^{\frac{1}{6}} \times 3^{- \frac{2}{3}}} = \frac{9^{\frac{1}{3} \times 3^{\frac{2}{3}}}}{3^{\frac{1}{6}} \times 27^{\frac{1}{2}}} = \frac{(3^{2})^{\frac{1}{3} \times 3^{\frac{2}{3}}}}{3^{\frac{1}{6}} \times (3^{3})^{\frac{1}{2}}} = \frac{3^{\frac{2}{3} + \frac{2}{3}}}{3^{\frac{1}{6} + \frac{3}{2}}} = \frac{3^{\frac{4}{3}}}{3^{\frac{1 + 9}{6}}} = \frac{3^{\frac{4}{3}}}{3^{\frac{10}{6}}} = \frac{3^{\frac{4}{3}}}{3^{\frac{5}{3}}} = 3^{\frac{4}{3} - \frac{5}{3}} = (3)^{- \frac{1}{3}}$

Suggest Corrections

Similar questions

Q. Solve

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

Q. Simplify

\frac{9^{\frac{1}{3}} * 27^{\frac{- 1}{2}}}{3^{\frac{1}{6}} * 3^{\frac{- 2}{3}}}

Q. Solve

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

Q. Solve

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

Simplify
$\frac{(0.3)^{\frac{1}{3}} {(\frac{1}{27})}^{\frac{1}{4}} (9)^{\frac{1}{6}} (0.81)^{\frac{2}{3}}}{(0.9)^{\frac{2}{3}} (3)^{- \frac{1}{2}} {(\frac{1}{3})}^{- 2} (243)^{- \frac{1}{4}}}$

Join BYJU'S Learning Program

Simplify:913×2712316×3−23

The correct option is C 32 913×2712316×3−23=913×323316×2712=(32)13×323316×(33)12=323+23316+32=34331+96=3433106=343353=343−53=(3)−13

Simplify: $\frac{9^{\frac{1}{3} \times 27^{\frac{1}{2}}}}{3^{\frac{1}{6}} \times 3^{- \frac{2}{3}}}$