Question

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

Please solve with COMPLETE steps and solutions

Answer 1

Answer:

$3^{(1/6)}$ ≈ 1.201

Step-by-step explanation:

Answer 2

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

To find :  Simplify

Solution:

Solving numerator 1st

$9^{\frac{1}{3}} = (3^2)^{\frac{1}{3}} = 3^{\frac{2}{3}}$

$27^{\frac{-1}{3} } = (3^3)^{\frac{-1}{3} } = 3^{-1}$

$3^{\frac{2}{3}} \times 3^{-1} = 3^{\frac{ 2}{3} - 1 } = 3^{\frac{-1}{3}$

now Solving denominator

${3^{\frac{1}{6} } \times 3^{\frac{-2}{3} } } = {3^{\frac{1}{6} +\frac{-2}{3} } = 3^{\frac{-3}{6} } = 3^{\frac{-1}{2} }$

Hence

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

= $3^{\frac{-1}{3} + \frac{1}{2 } } = 3^{\frac{1}{6}$

= $3^{\frac{1}{6}$

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

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