Question

27 ki power -2/3÷16ki power1/4​

Answer 1

Answer:

$\frac{27^{\frac{-2}{3}}}{(16)^{\frac{1}{4}}}=\frac{1}{18}$

Step-by-step explanation:

$\frac{27^{\frac{-2}{3}}}{(16)^{\frac{1}{4}}}$

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

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

$=\frac{3^{-2}}{2}\\=\frac{1}{2\times 3^{2}}\\=\frac{1}{2\times 9}\\=\frac{1}{18}$

Therefore,

$\frac{27^{\frac{-2}{3}}}{(16)^{\frac{1}{4}}}=\frac{1}{18}$

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Answer 2

Answer:

$\dfrac{27^{-2/3}}{16^{1/4}}=\dfrac{1}{18}$

Step-by-step explanation:

We need to find the value of $\dfrac{27^{-2/3}}{16^{1/4}}$

We know that,

$(3)^3=27\\\\(2)^4=16$

Using the above conversions, we get :

$\dfrac{27^{-2/3}}{16^{1/4}}=\dfrac{((3)^3)^{-2/3}}{((2)^4)^{1/4}}\\\\\dfrac{27^{-2/3}}{16^{1/4}}=\dfrac{3^{-2}}{2}\\\\=\dfrac{1}{3^2\times 2}\\\\=\dfrac{1}{9\times 2}\\\\=\dfrac{1}{18}$

So, $\dfrac{27^{-2/3}}{16^{1/4}}=\dfrac{1}{18}$