(2)^{-1}+[2/3-2^-1*((2/3)^-2*2/3+5^0)]^-1= eching

$$( 2 ) ^ { - 1 } + [ \frac { 2 } { 3 } - 2 ^ { - 1 } \cdot ( ( \frac { 2 } { 3 } ) ^ { - 2 } \cdot \frac { 2 } { 3 } + 5 ^ { 0 } ) ] ^ { - 1 } =$$

Baholash

$$-\frac{17}{14}\approx -1,214285714$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -2 va 1 ni qo‘shib, -1 ni oling.

$$2^{-1}+\left(\frac{2}{3}-2^{-1}\left(\left(\frac{2}{3}\right)^{-1}+5^{0}\right)\right)^{-1}$$

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

$$\frac{1}{2}+\left(\frac{2}{3}-2^{-1}\left(\left(\frac{2}{3}\right)^{-1}+5^{0}\right)\right)^{-1}$$

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

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{1}{2}\left(\left(\frac{2}{3}\right)^{-1}+5^{0}\right)\right)^{-1}$$

-1 daraja ko‘rsatkichini \frac{2}{3} ga hisoblang va \frac{3}{2} ni qiymatni oling.

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{1}{2}\left(\frac{3}{2}+5^{0}\right)\right)^{-1}$$

0 daraja ko‘rsatkichini 5 ga hisoblang va 1 ni qiymatni oling.

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{1}{2}\left(\frac{3}{2}+1\right)\right)^{-1}$$

\frac{5}{2} olish uchun \frac{3}{2} va 1'ni qo'shing.

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

\frac{5}{4} hosil qilish uchun \frac{1}{2} va \frac{5}{2} ni ko'paytirish.

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

-\frac{7}{12} olish uchun \frac{2}{3} dan \frac{5}{4} ni ayirish.

$$\frac{1}{2}+\left(-\frac{7}{12}\right)^{-1}$$

-1 daraja ko‘rsatkichini -\frac{7}{12} ga hisoblang va -\frac{12}{7} ni qiymatni oling.

$$\frac{1}{2}-\frac{12}{7}$$

-\frac{17}{14} olish uchun \frac{1}{2} dan \frac{12}{7} ni ayirish.

$$-\frac{17}{14}$$

Omil

$$-\frac{17}{14} = -1\frac{3}{14} = -1,2142857142857142$$