Question

Find the value of ${\displaystyle \frac{4}{{\left(216\right)}^{-\frac{2}{3}}}+\frac{1}{{\left(256\right)}^{-\frac{3}{4}}}+\frac{2}{{\left(243\right)}^{-\frac{1}{5}}}}$

Answer 1

${\displaystyle \frac{4}{{\left(216\right)}^{-\frac{2}{3}}}+\frac{1}{{\left(256\right)}^{-\frac{3}{4}}}+\frac{2}{{\left(243\right)}^{-\frac{1}{5}}}}$

⇒ ${\displaystyle 4\times {\left(216\right)}^{\frac{2}{3}}+{\left(256\right)}^{\frac{3}{4}}+2\times {\left(243\right)}^{\frac{1}{5}}}$

⇒ ${\displaystyle 4\times {\left(6^3\right)}^{\frac{2}{3}}+{\left(4^4\right)}^{\frac{3}{4}}+2\times {\left(3^5\right)}^{\frac{1}{5}}}$

By law indices (a^m)ⁿ = a^mn

⇒ 4 × (6)² + (4)² + 2 × (3)¹

⇒ 4 × 36 + (4)³ + 2 × (3)¹

= 144 + 64 + 6

= 214