{left(81y^10/16x^12right)}^frac{1{2}} eching

$${ \left( \frac{ 81 { y }^{ 10 } }{ 16 { x }^{ 12 } } \right) }^{ \frac{ 1 }{ 2 } }$$

Baholash

$$\frac{9\left(|y|\right)^{5}}{4x^{6}}$$

Yechim qadamlari

\frac{81y^{10}}{16x^{12}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(81y^{10}\right)^{\frac{1}{2}}}{\left(16x^{12}\right)^{\frac{1}{2}}}$$

\left(81y^{10}\right)^{\frac{1}{2}} ni kengaytirish.

$$\frac{81^{\frac{1}{2}}\left(y^{10}\right)^{\frac{1}{2}}}{\left(16x^{12}\right)^{\frac{1}{2}}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 10 va \frac{1}{2} ni ko‘paytirib, 5 ni oling.

$$\frac{81^{\frac{1}{2}}y^{5}}{\left(16x^{12}\right)^{\frac{1}{2}}}$$

\frac{1}{2} daraja ko‘rsatkichini 81 ga hisoblang va 9 ni qiymatni oling.

$$\frac{9y^{5}}{\left(16x^{12}\right)^{\frac{1}{2}}}$$

\left(16x^{12}\right)^{\frac{1}{2}} ni kengaytirish.

$$\frac{9y^{5}}{16^{\frac{1}{2}}\left(x^{12}\right)^{\frac{1}{2}}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 12 va \frac{1}{2} ni ko‘paytirib, 6 ni oling.

$$\frac{9y^{5}}{16^{\frac{1}{2}}x^{6}}$$

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

$$\frac{9y^{5}}{4x^{6}}$$

x ga nisbatan hosilani topish

$$-\frac{27\left(|y|\right)^{5}}{2x^{7}}$$