Question

simplify (16/9)^1/2 / (256/81)^-1/4 + √3/√27

Answer 1

Answer:

{(4/3)^2}^1/2÷{(4/3)^4}^-1/4 +√3/√27

Step-by-step explanation:

(4/3)^2×1/2×(4/3)^4×1/4+√3/3√3

4/3×4/3+1/3

16/9+1/3

(16+3)/9

19/9

Answer 2

 $Simplify \ \frac{(\frac{16}{9} )^{\frac{1}{2} } }{(\frac{256}{81} )^{(-\frac{1}{4}) } }+\frac{\sqrt{3} }{\sqrt{27} } .$

Step-by-step explanation:

Given:

$\ \frac{(\frac{16}{9} )^{\frac{1}{2} } }{(\frac{256}{81} )^{(-\frac{1}{4}) } }+\frac{\sqrt{3} }{\sqrt{27} } .$

To Find:

It is to be  simplify  $\ \frac{(\frac{16}{9} )^{\frac{1}{2} } }{(\frac{256}{81} )^{(-\frac{1}{4}) } }+\frac{\sqrt{3} }{\sqrt{27} } .$

Solution:

As given,$\ \frac{(\frac{16}{9} )^{\frac{1}{2} } }{(\frac{256}{81} )^{(-\frac{1}{4}) } }+\frac{\sqrt{3} }{\sqrt{27} } .$

$\ \frac{(\frac{16}{9} )^{\frac{1}{2} } }{(\frac{256}{81} )^{(-\frac{1}{4}) } }+\frac{\sqrt{3} }{\sqrt{27} }$

$=\ \frac{((\frac{4}{3} )^{2} )^{\frac{1}{2} } }{((\frac{4}{3})^{4} )^{(-\frac{1}{4}) } }+\frac{\sqrt{3} }{3\sqrt {3} }$

$=\frac{(\frac{4}{3} )^{2\times\frac{1}{2} } }{(\frac{4}{3} )^{4\times(-\frac{1}{4} )} } +\frac{1}{3}$

$=\frac{(\frac{4}{3} )}{(\frac{4}{3} )^{-1} } +\frac{1}{3}$

$=(\frac{4}{3} )^{2} +\frac{1}{3}$

$=\frac{16}{9} +\frac{1}{3}$

$=\frac{16+3}{9}$

$=\frac{19}{9}$

Thus, the value of $\ \frac{(\frac{16}{9} )^{\frac{1}{2} } }{(\frac{256}{81} )^{(-\frac{1}{4}) } }+\frac{\sqrt{3} }{\sqrt{27} }$ is  $\frac{19}{9}$.

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