Question

4/(216)^-2/3 - 1/(256)^ -3/4​

Answer 1

Answer:

4/(216)⁻²/³ + 1/(256)⁻³/⁴ + 2/(243)⁻¹/⁵ = 214

Step-by-step explanation:

/(216)⁻²/³ + 1/(256)⁻³/⁴ + 2/(243)⁻¹/⁵

Taking one term at a time, we solve as follows:

4/ (216)⁻²/³ = 4 / (216)⁻²/³ = 4 * 216²/³ = 4 * (6³)²/³ = 4 * 6² = 144

1/ (256)⁻³/⁴ = (256)³/⁴ = (4⁴)³/⁴ = 4³ = 64

2/(243)⁻¹/⁵ = 2 * (243)¹/⁵ = 2 * (3⁵)¹/⁵  = 2 * 3 = 6

4/(216)⁻²/³ + 1/(256)⁻³/⁴ + 2/(243)⁻¹/⁵ = 144 + 64 + 6 = 214

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

$\textsf{We have,}$

$\sf{ \frac{4}{(216 {)}^{ - \frac{ 2}{3} } } - \frac{1}{(256 {)}^{ - \frac{3}{4} } }}$

$\sf{ = \frac{4}{( {6}^{3} {)}^{ \frac{ - 2}{3} } } - \frac{1}{( {4}^{4} {)}^{ \frac{ - 3}{4} } }}$

$\sf{ = \frac{4}{( {6}{)}^{ \cancel{3}\times \frac{ - 2}{ \cancel{3}} } } - \frac{1}{( {4} {)}^{ \cancel{4} \times \frac{ - 3}{ \cancel{4}} } }}$

$\sf{ = \frac{4}{( {6})^{ - 2} } - \frac{1}{( {4})^{ - 3} }}$

$\sf{ = 4(6 {)}^{2} - (4 {)}^{3} }$

$\sf{ = 4 \times 36 - 64}$

$\sf{ = 144 - 64}$

$\sf{ = 80} \: \: \: \bf{Ans.}$