frac{(9x^{3})^{1/2}*(x^frac{1{2}})^-1}{(3x^frac{1{2}})^2} eching

$$\frac { ( 9 x ^ { 3 } ) ^ { \frac { 1 } { 2 } } \times ( x ^ { \frac { 1 } { 2 } } ) ^ { - 1 } } { ( 3 x ^ { \frac { 1 } { 2 } } ) ^ { 2 } }$$

Baholash

$$\frac{1}{3}\approx 0,333333333$$

Yechim qadamlari

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

$$\frac{\left(9x^{3}\right)^{\frac{1}{2}}x^{-\frac{1}{2}}}{\left(3x^{\frac{1}{2}}\right)^{2}}$$

\left(9x^{3}\right)^{\frac{1}{2}} ni kengaytirish.

$$\frac{9^{\frac{1}{2}}\left(x^{3}\right)^{\frac{1}{2}}x^{-\frac{1}{2}}}{\left(3x^{\frac{1}{2}}\right)^{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va \frac{1}{2} ni ko‘paytirib, \frac{3}{2} ni oling.

$$\frac{9^{\frac{1}{2}}x^{\frac{3}{2}}x^{-\frac{1}{2}}}{\left(3x^{\frac{1}{2}}\right)^{2}}$$

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

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

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{3}{2} va -\frac{1}{2} ni qo‘shib, 1 ni oling.

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

\left(3x^{\frac{1}{2}}\right)^{2} ni kengaytirish.

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

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

$$\frac{3x^{1}}{3^{2}x^{1}}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$\frac{3x^{1}}{9x^{1}}$$

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

$$\frac{3x^{1}}{9x}$$

Surat va maxrajdagi ikkala 3x^{1} ni qisqartiring.

$$\frac{1}{3}$$

x ga nisbatan hosilani topish

$$0$$