((-1/4)^{3}:(-1/4)+(2-1/2)^{4}(1-5/9)^2):[(frac{17}{2})^4:(frac{17}{2})^3+frac{3}{2}*(-1)^2-1+frac{1}{4}]*frac{37}{2} eching

$$( ( - \frac { 1 } { 4 } ) ^ { 3 } : ( - \frac { 1 } { 4 } ) + ( 2 - \frac { 1 } { 2 } ) ^ { 4 } ( 1 - \frac { 5 } { 9 } ) ^ { 2 } ) : [ ( \frac { 17 } { 2 } ) ^ { 4 } : ( \frac { 17 } { 2 } ) ^ { 3 } + \frac { 3 } { 2 } \cdot ( - 1 ) ^ { 2 } - 1 + \frac { 1 } { 4 } ] \cdot \frac { 37 } { 2 }$$

Baholash

$$\frac{17}{8}=2,125$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 3 dan 1 ni ayirib, 2 ni oling.

$$\frac{\left(-\frac{1}{4}\right)^{2}+\left(2-\frac{1}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\frac{\left(\frac{17}{2}\right)^{4}}{\left(\frac{17}{2}\right)^{3}}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 4 dan 3 ni ayirib, 1 ni oling.

$$\frac{\left(-\frac{1}{4}\right)^{2}+\left(2-\frac{1}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

2 daraja ko‘rsatkichini -\frac{1}{4} ga hisoblang va \frac{1}{16} ni qiymatni oling.

$$\frac{\frac{1}{16}+\left(2-\frac{1}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

\frac{3}{2} olish uchun 2 dan \frac{1}{2} ni ayirish.

$$\frac{\frac{1}{16}+\left(\frac{3}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

4 daraja ko‘rsatkichini \frac{3}{2} ga hisoblang va \frac{81}{16} ni qiymatni oling.

$$\frac{\frac{1}{16}+\frac{81}{16}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

\frac{4}{9} olish uchun 1 dan \frac{5}{9} ni ayirish.

$$\frac{\frac{1}{16}+\frac{81}{16}\times \left(\frac{4}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

2 daraja ko‘rsatkichini \frac{4}{9} ga hisoblang va \frac{16}{81} ni qiymatni oling.

$$\frac{\frac{1}{16}+\frac{81}{16}\times \frac{16}{81}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

1 hosil qilish uchun \frac{81}{16} va \frac{16}{81} ni ko'paytirish.

$$\frac{\frac{1}{16}+1}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

\frac{17}{16} olish uchun \frac{1}{16} va 1'ni qo'shing.

$$\frac{\frac{17}{16}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

1 daraja ko‘rsatkichini \frac{17}{2} ga hisoblang va \frac{17}{2} ni qiymatni oling.

$$\frac{\frac{17}{16}}{\frac{17}{2}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

2 daraja ko‘rsatkichini -1 ga hisoblang va 1 ni qiymatni oling.

$$\frac{\frac{17}{16}}{\frac{17}{2}+\frac{3}{2}\times 1-1+\frac{1}{4}}\times \frac{37}{2}$$

\frac{3}{2} hosil qilish uchun \frac{3}{2} va 1 ni ko'paytirish.

$$\frac{\frac{17}{16}}{\frac{17}{2}+\frac{3}{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

10 olish uchun \frac{17}{2} va \frac{3}{2}'ni qo'shing.

$$\frac{\frac{17}{16}}{10-1+\frac{1}{4}}\times \frac{37}{2}$$

9 olish uchun 10 dan 1 ni ayirish.

$$\frac{\frac{17}{16}}{9+\frac{1}{4}}\times \frac{37}{2}$$

\frac{37}{4} olish uchun 9 va \frac{1}{4}'ni qo'shing.

$$\frac{\frac{17}{16}}{\frac{37}{4}}\times \frac{37}{2}$$

\frac{17}{16} ni \frac{37}{4} ga bo'lish \frac{17}{16} ga k'paytirish \frac{37}{4} ga qaytarish.

$$\frac{17}{16}\times \frac{4}{37}\times \frac{37}{2}$$

\frac{17}{148} hosil qilish uchun \frac{17}{16} va \frac{4}{37} ni ko'paytirish.

$$\frac{17}{148}\times \frac{37}{2}$$

\frac{17}{8} hosil qilish uchun \frac{17}{148} va \frac{37}{2} ni ko'paytirish.

$$\frac{17}{8}$$

Omil

$$\frac{17}{2 ^ {3}} = 2\frac{1}{8} = 2,125$$