(3x^{3}y^{-2}z^{-1})^-2(5xy^-2z^-1)^2 eching

$$( 3 x ^ { 3 } y ^ { - 2 } z ^ { - 1 } ) ^ { - 2 } ( 5 x y ^ { - 2 } z ^ { - 1 } ) ^ { 2 }$$

Baholash

$$\frac{25}{9x^{4}}$$

Yechim qadamlari

\left(3x^{3}y^{-2}z^{-1}\right)^{-2} ni kengaytirish.

$$3^{-2}\left(x^{3}\right)^{-2}\left(y^{-2}\right)^{-2}\left(z^{-1}\right)^{-2}\times \left(5xy^{-2}z^{-1}\right)^{2}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va -2 ni ko‘paytirib, -6 ni oling.

$$3^{-2}x^{-6}\left(y^{-2}\right)^{-2}\left(z^{-1}\right)^{-2}\times \left(5xy^{-2}z^{-1}\right)^{2}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -2 va -2 ni ko‘paytirib, 4 ni oling.

$$3^{-2}x^{-6}y^{4}\left(z^{-1}\right)^{-2}\times \left(5xy^{-2}z^{-1}\right)^{2}$$

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

$$3^{-2}x^{-6}y^{4}z^{2}\times \left(5xy^{-2}z^{-1}\right)^{2}$$

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

$$\frac{1}{9}x^{-6}y^{4}z^{2}\times \left(5xy^{-2}z^{-1}\right)^{2}$$

\left(5xy^{-2}z^{-1}\right)^{2} ni kengaytirish.

$$\frac{1}{9}x^{-6}y^{4}z^{2}\times 5^{2}x^{2}\left(y^{-2}\right)^{2}\left(z^{-1}\right)^{2}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -2 va 2 ni ko‘paytirib, -4 ni oling.

$$\frac{1}{9}x^{-6}y^{4}z^{2}\times 5^{2}x^{2}y^{-4}\left(z^{-1}\right)^{2}$$

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

$$\frac{1}{9}x^{-6}y^{4}z^{2}\times 5^{2}x^{2}y^{-4}z^{-2}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{1}{9}x^{-6}y^{4}z^{2}\times 25x^{2}y^{-4}z^{-2}$$

\frac{25}{9} hosil qilish uchun \frac{1}{9} va 25 ni ko'paytirish.

$$\frac{25}{9}x^{-6}y^{4}z^{2}x^{2}y^{-4}z^{-2}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -6 va 2 ni qo‘shib, -4 ni oling.

$$\frac{25}{9}x^{-4}y^{4}z^{2}y^{-4}z^{-2}$$

1 hosil qilish uchun y^{4} va y^{-4} ni ko'paytirish.

$$\frac{25}{9}x^{-4}z^{2}z^{-2}$$

1 hosil qilish uchun z^{2} va z^{-2} ni ko'paytirish.

$$\frac{25}{9}x^{-4}$$

Kengaytirish

$$\frac{25}{9x^{4}}$$

Yechim qadamlari

\left(3x^{3}y^{-2}z^{-1}\right)^{-2} ni kengaytirish.

$$3^{-2}\left(x^{3}\right)^{-2}\left(y^{-2}\right)^{-2}\left(z^{-1}\right)^{-2}\times \left(5xy^{-2}z^{-1}\right)^{2}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va -2 ni ko‘paytirib, -6 ni oling.

$$3^{-2}x^{-6}\left(y^{-2}\right)^{-2}\left(z^{-1}\right)^{-2}\times \left(5xy^{-2}z^{-1}\right)^{2}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -2 va -2 ni ko‘paytirib, 4 ni oling.

$$3^{-2}x^{-6}y^{4}\left(z^{-1}\right)^{-2}\times \left(5xy^{-2}z^{-1}\right)^{2}$$

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

$$3^{-2}x^{-6}y^{4}z^{2}\times \left(5xy^{-2}z^{-1}\right)^{2}$$

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

$$\frac{1}{9}x^{-6}y^{4}z^{2}\times \left(5xy^{-2}z^{-1}\right)^{2}$$

\left(5xy^{-2}z^{-1}\right)^{2} ni kengaytirish.

$$\frac{1}{9}x^{-6}y^{4}z^{2}\times 5^{2}x^{2}\left(y^{-2}\right)^{2}\left(z^{-1}\right)^{2}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -2 va 2 ni ko‘paytirib, -4 ni oling.

$$\frac{1}{9}x^{-6}y^{4}z^{2}\times 5^{2}x^{2}y^{-4}\left(z^{-1}\right)^{2}$$

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

$$\frac{1}{9}x^{-6}y^{4}z^{2}\times 5^{2}x^{2}y^{-4}z^{-2}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{1}{9}x^{-6}y^{4}z^{2}\times 25x^{2}y^{-4}z^{-2}$$

\frac{25}{9} hosil qilish uchun \frac{1}{9} va 25 ni ko'paytirish.

$$\frac{25}{9}x^{-6}y^{4}z^{2}x^{2}y^{-4}z^{-2}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -6 va 2 ni qo‘shib, -4 ni oling.

$$\frac{25}{9}x^{-4}y^{4}z^{2}y^{-4}z^{-2}$$

1 hosil qilish uchun y^{4} va y^{-4} ni ko'paytirish.

$$\frac{25}{9}x^{-4}z^{2}z^{-2}$$

1 hosil qilish uchun z^{2} va z^{-2} ni ko'paytirish.

$$\frac{25}{9}x^{-4}$$