[4x^-2/9y^-4]^-frac{5{2}} eching

$$[ \frac { 4 x ^ { - 2 } } { 9 y ^ { - 4 } } ] ^ { - \frac { 5 } { 2 } }$$

Baholash

$$\frac{243\left(|x|\right)^{5}}{32y^{10}}$$

Yechim qadamlari

\frac{4x^{-2}}{9y^{-4}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(4x^{-2}\right)^{-\frac{5}{2}}}{\left(9y^{-4}\right)^{-\frac{5}{2}}}$$

\left(4x^{-2}\right)^{-\frac{5}{2}} ni kengaytirish.

$$\frac{4^{-\frac{5}{2}}\left(x^{-2}\right)^{-\frac{5}{2}}}{\left(9y^{-4}\right)^{-\frac{5}{2}}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -2 va -\frac{5}{2} ni ko‘paytirib, 5 ni oling.

$$\frac{4^{-\frac{5}{2}}x^{5}}{\left(9y^{-4}\right)^{-\frac{5}{2}}}$$

-\frac{5}{2} daraja ko‘rsatkichini 4 ga hisoblang va \frac{1}{32} ni qiymatni oling.

$$\frac{\frac{1}{32}x^{5}}{\left(9y^{-4}\right)^{-\frac{5}{2}}}$$

\left(9y^{-4}\right)^{-\frac{5}{2}} ni kengaytirish.

$$\frac{\frac{1}{32}x^{5}}{9^{-\frac{5}{2}}\left(y^{-4}\right)^{-\frac{5}{2}}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -4 va -\frac{5}{2} ni ko‘paytirib, 10 ni oling.

$$\frac{\frac{1}{32}x^{5}}{9^{-\frac{5}{2}}y^{10}}$$

-\frac{5}{2} daraja ko‘rsatkichini 9 ga hisoblang va \frac{1}{243} ni qiymatni oling.

$$\frac{\frac{1}{32}x^{5}}{\frac{1}{243}y^{10}}$$

x ga nisbatan hosilani topish

$$\frac{1215|x|x^{3}}{32y^{10}}$$