2^-1[(5/3)^4+(3/5)^-2]div17/9 eching

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

Baholash

$$\frac{25}{9}\approx 2,777777778$$

Yechim qadamlari

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

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

4 daraja ko‘rsatkichini \frac{5}{3} ga hisoblang va \frac{625}{81} ni qiymatni oling.

$$\frac{\frac{1}{2}\left(\frac{625}{81}+\left(\frac{3}{5}\right)^{-2}\right)}{\frac{17}{9}}$$

-2 daraja ko‘rsatkichini \frac{3}{5} ga hisoblang va \frac{25}{9} ni qiymatni oling.

$$\frac{\frac{1}{2}\left(\frac{625}{81}+\frac{25}{9}\right)}{\frac{17}{9}}$$

\frac{850}{81} olish uchun \frac{625}{81} va \frac{25}{9}'ni qo'shing.

$$\frac{\frac{1}{2}\times \frac{850}{81}}{\frac{17}{9}}$$

\frac{425}{81} hosil qilish uchun \frac{1}{2} va \frac{850}{81} ni ko'paytirish.

$$\frac{\frac{425}{81}}{\frac{17}{9}}$$

\frac{425}{81} ni \frac{17}{9} ga bo'lish \frac{425}{81} ga k'paytirish \frac{17}{9} ga qaytarish.

$$\frac{425}{81}\times \frac{9}{17}$$

\frac{25}{9} hosil qilish uchun \frac{425}{81} va \frac{9}{17} ni ko'paytirish.

$$\frac{25}{9}$$

Omil

$$\frac{5 ^ {2}}{3 ^ {2}} = 2\frac{7}{9} = 2,7777777777777777$$