-(1/3+frac{7/9)^{2}}{(1-1/2)^{2}*(-2)^3-3/2}+[-(-frac{1}{6})^2+frac{frac{1}{4}-frac{1}{5}}{(1-frac{2}{5})^2}]^2-frac{frac{1}{3}-frac{2}{9}}{frac{1}{8}-frac{15}{8}}=-এর সমাধান করুন

$$- \frac { ( \frac { 1 } { 3 } + \frac { 7 } { 9 } ) ^ { 2 } } { ( 1 - \frac { 1 } { 2 } ) ^ { 2 } \cdot ( - 2 ) ^ { 3 } - \frac { 3 } { 2 } } + [ - ( - \frac { 1 } { 6 } ) ^ { 2 } + \frac { \frac { 1 } { 4 } - \frac { 1 } { 5 } } { ( 1 - \frac { 2 } { 5 } ) ^ { 2 } } ] ^ { 2 } - \frac { \frac { 1 } { 3 } - \frac { 2 } { 9 } } { \frac { 1 } { 8 } - \frac { 15 } { 8 } } =$$

মূল্যায়ন করুন

$$\frac{3}{7}\approx 0.428571429$$

সমাধানের ধাপগুলো

\frac{10}{9} পেতে \frac{1}{3} এবং \frac{7}{9} যোগ করুন।

$$-\frac{\left(\frac{10}{9}\right)^{2}}{\left(1-\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}+\left(-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

2 এর ঘাতে \frac{10}{9} গণনা করুন এবং \frac{100}{81} পান।

$$-\frac{\frac{100}{81}}{\left(1-\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}+\left(-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{1}{2} পেতে 1 থেকে \frac{1}{2} বাদ দিন।

$$-\frac{\frac{100}{81}}{\left(\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}+\left(-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

2 এর ঘাতে \frac{1}{2} গণনা করুন এবং \frac{1}{4} পান।

$$-\frac{\frac{100}{81}}{\frac{1}{4}\left(-2\right)^{3}-\frac{3}{2}}+\left(-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

3 এর ঘাতে -2 গণনা করুন এবং -8 পান।

$$-\frac{\frac{100}{81}}{\frac{1}{4}\left(-8\right)-\frac{3}{2}}+\left(-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

-2 পেতে \frac{1}{4} এবং -8 গুণ করুন।

$$-\frac{\frac{100}{81}}{-2-\frac{3}{2}}+\left(-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

-\frac{7}{2} পেতে -2 থেকে \frac{3}{2} বাদ দিন।

$$-\frac{\frac{100}{81}}{-\frac{7}{2}}+\left(-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

-\frac{7}{2} এর বিপরীত দিয়ে \frac{100}{81} কে গুণ করার মাধ্যমে \frac{100}{81} কে -\frac{7}{2} দিয়ে ভাগ দিয়ে ভাগ করুন।

$$-\frac{100}{81}\left(-\frac{2}{7}\right)+\left(-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

-\frac{200}{567} পেতে \frac{100}{81} এবং -\frac{2}{7} গুণ করুন।

$$-\left(-\frac{200}{567}\right)+\left(-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

-\frac{200}{567}-এর বিপরীত হলো \frac{200}{567}।

$$\frac{200}{567}+\left(-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

2 এর ঘাতে -\frac{1}{6} গণনা করুন এবং \frac{1}{36} পান।

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{1}{20} পেতে \frac{1}{4} থেকে \frac{1}{5} বাদ দিন।

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{3}{5} পেতে 1 থেকে \frac{2}{5} বাদ দিন।

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

2 এর ঘাতে \frac{3}{5} গণনা করুন এবং \frac{9}{25} পান।

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{\frac{1}{20}}{\frac{9}{25}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{9}{25} এর বিপরীত দিয়ে \frac{1}{20} কে গুণ করার মাধ্যমে \frac{1}{20} কে \frac{9}{25} দিয়ে ভাগ দিয়ে ভাগ করুন।

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{1}{20}\times \frac{25}{9}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{5}{36} পেতে \frac{1}{20} এবং \frac{25}{9} গুণ করুন।

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{5}{36}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{1}{9} পেতে -\frac{1}{36} এবং \frac{5}{36} যোগ করুন।

$$\frac{200}{567}+\left(\frac{1}{9}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

2 এর ঘাতে \frac{1}{9} গণনা করুন এবং \frac{1}{81} পান।

$$\frac{200}{567}+\frac{1}{81}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{23}{63} পেতে \frac{200}{567} এবং \frac{1}{81} যোগ করুন।

$$\frac{23}{63}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

\frac{1}{9} পেতে \frac{1}{3} থেকে \frac{2}{9} বাদ দিন।

$$\frac{23}{63}-\frac{\frac{1}{9}}{\frac{1}{8}-\frac{15}{8}}$$

-\frac{7}{4} পেতে \frac{1}{8} থেকে \frac{15}{8} বাদ দিন।

$$\frac{23}{63}-\frac{\frac{1}{9}}{-\frac{7}{4}}$$

-\frac{7}{4} এর বিপরীত দিয়ে \frac{1}{9} কে গুণ করার মাধ্যমে \frac{1}{9} কে -\frac{7}{4} দিয়ে ভাগ দিয়ে ভাগ করুন।

$$\frac{23}{63}-\frac{1}{9}\left(-\frac{4}{7}\right)$$

-\frac{4}{63} পেতে \frac{1}{9} এবং -\frac{4}{7} গুণ করুন।

$$\frac{23}{63}-\left(-\frac{4}{63}\right)$$

-\frac{4}{63}-এর বিপরীত হলো \frac{4}{63}।

$$\frac{23}{63}+\frac{4}{63}$$

\frac{3}{7} পেতে \frac{23}{63} এবং \frac{4}{63} যোগ করুন।

$$\frac{3}{7}$$

ভাঙা

$$\frac{3}{7} = 0.42857142857142855$$