Question

simplify:4/216-2/3+2/243-1/5+1/256-3/4
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Answer 1

Answer:

Step-by-step explanation:

4/216 -2/3 +2/243 - 1/5 + 1/256 -3/4

1/54 - 2/3 + 2/243 - 1/5 + 1/256 - 3/4

(1-36)/54 + (10 - 243)/1215 + (1-192)/256

-35/54  -233/1215 -192/256

(-1575 -466)/2430 - 192/256

-2041/2430 -192/256

(-261248 - 233280)/ 311040

-484528/311040

1.557 or 1.56

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

$\textsf{We have,}$

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

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

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

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

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

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

$\sf{ = 144 - 64}$

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