Question

FIND THE VALUE OF 4/(216) RASE TO THE POWER -2/3 - 1/(256) RASE TO THE POWER -3/4

Answer 1

Solution:-
4/(216)⁻²/³ - 1/(256)⁻³/⁴
4/(6³)⁻²/³ - 1/(4⁴)⁻³/⁴
4/(6)⁻² - 1/(4)⁻³
4 × (6)² - 1 × (4)³
(4 ×36) - 64
144 - 64
80  Answer

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

$\textsf{We have,}$

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

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

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

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

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

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

$\sf{ = 144 - 64}$

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