Question

(-1/2)^2×(2/3)^3÷(3/4)^2​

Answer 1

$\sf\red{Given :-}$

${\sf{ (\frac{ - 1}{2} })^{2} \times { (\frac{2}{3} })^{2} \div { (\frac{3}{4} })^{2}}$

$\sf\red{Solution :-}$

$:\implies{\sf{ (\frac{ - 1}{2} })^{2} \times { (\frac{2}{3} })^{2} \div { (\frac{3}{4} })^{2}}$

$:\implies{\sf{ \frac{1}{4} } \times {\frac{8}{27} } \div {\frac{9}{16} }}$

$:\implies{\sf{\frac{8}{108} } \div { \frac{9}{16} }}$

$:\implies{\sf{\frac{8}{108} } \times { \frac{16}{9} }}$

$:\implies{\sf{\frac{8}{\cancel{108}} } \times { \frac{\cancel{16}}{9} }}$

$:\implies{\sf{\frac{8}{27} } \times { \frac{4}{9} }}$

$:\implies{\sf{\boxed{\red{\frac{32}{243} }}}}$

$\sf\purple{Thank\:You\:!!}$

Answer 2

Answer:

[tex] ({ \frac{ - 1}{2} })^{2} \times ( { \frac{2}{3} })^{3} \div ( { \frac{3}{4} })^{2} \\ \\ = \frac{1}{4} \times \frac{8}{27} \div \frac{9}{16} \\ \\ = \frac{1}{4} \times \frac{8}{27} \times \frac{16}{9} = \frac{32}{243}