frac{2(a^{-2}b^{8})^-3*(ab)^-6}{(2b^-6)^2} eching

$$\frac { 2 ( a ^ { - 2 } b ^ { 8 } ) ^ { - 3 } \times ( a b ) ^ { - 6 } } { ( 2 b ^ { - 6 } ) ^ { 2 } }$$

Baholash

$$\frac{1}{2b^{18}}$$

Yechim qadamlari

\left(a^{-2}b^{8}\right)^{-3} ni kengaytirish.

$$\frac{2\left(a^{-2}\right)^{-3}\left(b^{8}\right)^{-3}\left(ab\right)^{-6}}{\left(2b^{-6}\right)^{2}}$$

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

$$\frac{2a^{6}\left(b^{8}\right)^{-3}\left(ab\right)^{-6}}{\left(2b^{-6}\right)^{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 8 va -3 ni ko‘paytirib, -24 ni oling.

$$\frac{2a^{6}b^{-24}\left(ab\right)^{-6}}{\left(2b^{-6}\right)^{2}}$$

\left(ab\right)^{-6} ni kengaytirish.

$$\frac{2a^{6}b^{-24}a^{-6}b^{-6}}{\left(2b^{-6}\right)^{2}}$$

1 hosil qilish uchun a^{6} va a^{-6} ni ko'paytirish.

$$\frac{2b^{-24}b^{-6}}{\left(2b^{-6}\right)^{2}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -24 va -6 ni qo‘shib, -30 ni oling.

$$\frac{2b^{-30}}{\left(2b^{-6}\right)^{2}}$$

\left(2b^{-6}\right)^{2} ni kengaytirish.

$$\frac{2b^{-30}}{2^{2}\left(b^{-6}\right)^{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -6 va 2 ni ko‘paytirib, -12 ni oling.

$$\frac{2b^{-30}}{2^{2}b^{-12}}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{2b^{-30}}{4b^{-12}}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{b^{-30}}{2b^{-12}}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\frac{1}{2b^{18}}$$

Kengaytirish

$$\frac{1}{2b^{18}}$$

Yechim qadamlari

\left(a^{-2}b^{8}\right)^{-3} ni kengaytirish.

$$\frac{2\left(a^{-2}\right)^{-3}\left(b^{8}\right)^{-3}\left(ab\right)^{-6}}{\left(2b^{-6}\right)^{2}}$$

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

$$\frac{2a^{6}\left(b^{8}\right)^{-3}\left(ab\right)^{-6}}{\left(2b^{-6}\right)^{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 8 va -3 ni ko‘paytirib, -24 ni oling.

$$\frac{2a^{6}b^{-24}\left(ab\right)^{-6}}{\left(2b^{-6}\right)^{2}}$$

\left(ab\right)^{-6} ni kengaytirish.

$$\frac{2a^{6}b^{-24}a^{-6}b^{-6}}{\left(2b^{-6}\right)^{2}}$$

1 hosil qilish uchun a^{6} va a^{-6} ni ko'paytirish.

$$\frac{2b^{-24}b^{-6}}{\left(2b^{-6}\right)^{2}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -24 va -6 ni qo‘shib, -30 ni oling.

$$\frac{2b^{-30}}{\left(2b^{-6}\right)^{2}}$$

\left(2b^{-6}\right)^{2} ni kengaytirish.

$$\frac{2b^{-30}}{2^{2}\left(b^{-6}\right)^{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -6 va 2 ni ko‘paytirib, -12 ni oling.

$$\frac{2b^{-30}}{2^{2}b^{-12}}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{2b^{-30}}{4b^{-12}}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{b^{-30}}{2b^{-12}}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\frac{1}{2b^{18}}$$