Question

(8/27)^-1/3×(25/4)^1/2×(4/9)^0×(125/64)^1/3

Answer 1

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Answer 2

$(\dfrac{8}{27} )^{\dfrac{-1}{3}}\times (\dfrac{25}{4})^{\dfrac{1}{2}}\times (\dfrac{4}{9})^{0}\times (\dfrac{125}{64} )^{\dfrac{1}{3}}=\dfrac{75}{16}$

Step-by-step explanation:

We have,

$(\dfrac{8}{27} )^{\dfrac{-1}{3}}\times (\dfrac{25}{4})^{\dfrac{1}{2}}\times (\dfrac{4}{9})^{0}\times (\dfrac{125}{64} )^{\dfrac{1}{3}}$

To find, the value of $(\dfrac{8}{27} )^{\dfrac{-1}{3}}\times (\dfrac{25}{4})^{\dfrac{1}{2}}\times (\dfrac{4}{9})^{0}\times (\dfrac{125}{64} )^{\dfrac{1}{3}}=?$

∴ $(\dfrac{8}{27} )^{\dfrac{-1}{3}}\times (\dfrac{25}{4})^{\dfrac{1}{2}}\times (\dfrac{4}{9})^{0}\times (\dfrac{125}{64} )^{\dfrac{1}{3}}$

$=(\dfrac{27}{8} )^{3}\times \dfrac{5}{2}\times 1\times \sqrt[3]{\dfrac{125}{64}}$

[∵ $a^{0} =1$]

$=\sqrt[3]{\dfrac{27}{8}} \times \dfrac{5}{2}\times 1\times \sqrt[3]{\dfrac{5.5.5}{4.4.4}}$

$=\sqrt[3]{\dfrac{3.3.3}{2.2.2}} \times \dfrac{5}{2}\times \dfrac{5}{4}$

$=\dfrac{3}{2} \times \dfrac{25}{8}$

$=\dfrac{75}{16}$

Hence, $(\dfrac{8}{27} )^{\dfrac{-1}{3}}\times (\dfrac{25}{4})^{\dfrac{1}{2}}\times (\dfrac{4}{9})^{0}\times (\dfrac{125}{64} )^{\dfrac{1}{3}}=\dfrac{75}{16}$