Question

Simplify ( 8 /27 )raised to −2/ 3 × ( 4/ 9 ) raised to−3/ 2...?​

Answer 1

⇒ $(\frac{8}{27}) ^{\frac{-2}{3} }.(\frac{4}{9})^{\frac{-3}{2} }$

⇒ $(\frac{27}{8}) ^{\frac{2}{3} }.(\frac{9}{4} )^\frac{3}{2}$

⇒ $(\frac{3^3}{2^3})^\frac{2}{3} .(\frac{3^2}{2^2})^\frac{3}{2}$

⇒ $(\frac{3}{2} )^{3.\frac{2}{3} } .(\frac{3}{2})^{2.\frac{3}{2} }$

⇒ $(\frac{3}{2})^2 .(\frac{3}{2})^3$

⇒ $(\frac{3}{2})^{2+3}$

⇒ $(\frac{3}{2})^5$

⇒ $(\frac{3^5}{2^5})$

⇒ $(\frac{243}{32} )$

⇒ 7.59

Hope it helps :)