Question

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

• A. 196
• B. 208
• C. 248
• D. 214

Answer 1

The correct option is D 214

$\frac{4}{{216}^{\frac{-2}{3}}}$+$\frac{1}{{256}^{\frac{-3}{4}}}$+$\frac{2}{{243}^{\frac{-1}{5}}}$

= $(4\times (216{)}^{\frac{2}{3}})$ + $(1\times (256{)}^{\frac{3}{4}})$ + $(2\times (243{)}^{\frac{1}{5}})$ [∵ $\frac{1}{a^{-m}}=a^m$]

= $(4\times (2^3\times 3^3{)}^{\frac{2}{3}})$ + $(2^8{)}^{\frac{3}{4}}+(2\times \left(3^5{)}^{\frac{1}{5}}\right)$

= $(4\times 2^{3\times \frac{2}{3}}\times 3^{3\times \frac{2}{3}})$ + $2^{8\times \frac{3}{4}}$ + $(2\times 3^{5\times \frac{1}{5}})$
[∵ $a^{m^n}=a^{mn}$]

= $(4\times 2^2\times 3^2)$ + $2^6$ + $(2\times 3^1)$

= $144+64+6$

= $214$