(2/3)^{-4}*(2/3)^{-3}*(-3/2)^-5+8[(2-1/4)frac{1}{7}-frac{3}{4}]+[(-frac{3}{2})^2*(frac{1}{3})^2]^-1 eching

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

Baholash

$$-\frac{9}{4}=-2,25$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -4 va -3 ni qo‘shib, -7 ni oling.

$$\left(\frac{2}{3}\right)^{-7}\left(-\frac{3}{2}\right)^{-5}+8\left(\left(2-\frac{1}{4}\right)\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

-7 daraja ko‘rsatkichini \frac{2}{3} ga hisoblang va \frac{2187}{128} ni qiymatni oling.

$$\frac{2187}{128}\left(-\frac{3}{2}\right)^{-5}+8\left(\left(2-\frac{1}{4}\right)\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

-5 daraja ko‘rsatkichini -\frac{3}{2} ga hisoblang va -\frac{32}{243} ni qiymatni oling.

$$\frac{2187}{128}\left(-\frac{32}{243}\right)+8\left(\left(2-\frac{1}{4}\right)\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

-\frac{9}{4} hosil qilish uchun \frac{2187}{128} va -\frac{32}{243} ni ko'paytirish.

$$-\frac{9}{4}+8\left(\left(2-\frac{1}{4}\right)\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

\frac{7}{4} olish uchun 2 dan \frac{1}{4} ni ayirish.

$$-\frac{9}{4}+8\left(\frac{7}{4}\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

\frac{1}{4} hosil qilish uchun \frac{7}{4} va \frac{1}{7} ni ko'paytirish.

$$-\frac{9}{4}+8\left(\frac{1}{4}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

-\frac{1}{2} olish uchun \frac{1}{4} dan \frac{3}{4} ni ayirish.

$$-\frac{9}{4}+8\left(-\frac{1}{2}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

-4 hosil qilish uchun 8 va -\frac{1}{2} ni ko'paytirish.

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

-\frac{25}{4} olish uchun -\frac{9}{4} dan 4 ni ayirish.

$$-\frac{25}{4}+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

2 daraja ko‘rsatkichini -\frac{3}{2} ga hisoblang va \frac{9}{4} ni qiymatni oling.

$$-\frac{25}{4}+\left(\frac{9}{4}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

2 daraja ko‘rsatkichini \frac{1}{3} ga hisoblang va \frac{1}{9} ni qiymatni oling.

$$-\frac{25}{4}+\left(\frac{9}{4}\times \frac{1}{9}\right)^{-1}$$

\frac{1}{4} hosil qilish uchun \frac{9}{4} va \frac{1}{9} ni ko'paytirish.

$$-\frac{25}{4}+\left(\frac{1}{4}\right)^{-1}$$

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

$$-\frac{25}{4}+4$$

-\frac{9}{4} olish uchun -\frac{25}{4} va 4'ni qo'shing.

$$-\frac{9}{4}$$

Omil

$$-\frac{9}{4} = -2\frac{1}{4} = -2,25$$