[-3/2a^{3}b^{2}]^{4}*[a^2/3a^2b^5]^3 eching

$$[ - \frac { 3 } { 2 } a ^ { 3 } b ^ { 2 } ] ^ { 4 } \cdot [ \frac { a ^ { 2 } } { 3 } a ^ { 2 } b ^ { 5 } ] ^ { 3 }$$

Baholash

$$\frac{3b^{23}a^{24}}{16}$$

Yechim qadamlari

\left(-\frac{3}{2}a^{3}b^{2}\right)^{4} ni kengaytirish.

$$\left(-\frac{3}{2}\right)^{4}\left(a^{3}\right)^{4}\left(b^{2}\right)^{4}\times \left(\frac{a^{2}}{3}a^{2}b^{5}\right)^{3}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 4 ni ko‘paytirib, 12 ni oling.

$$\left(-\frac{3}{2}\right)^{4}a^{12}\left(b^{2}\right)^{4}\times \left(\frac{a^{2}}{3}a^{2}b^{5}\right)^{3}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 4 ni ko‘paytirib, 8 ni oling.

$$\left(-\frac{3}{2}\right)^{4}a^{12}b^{8}\times \left(\frac{a^{2}}{3}a^{2}b^{5}\right)^{3}$$

4 daraja ko‘rsatkichini -\frac{3}{2} ga hisoblang va \frac{81}{16} ni qiymatni oling.

$$\frac{81}{16}a^{12}b^{8}\times \left(\frac{a^{2}}{3}a^{2}b^{5}\right)^{3}$$

\frac{a^{2}}{3}a^{2} ni yagona kasrga aylantiring.

$$\frac{81}{16}a^{12}b^{8}\times \left(\frac{a^{2}a^{2}}{3}b^{5}\right)^{3}$$

\frac{a^{2}a^{2}}{3}b^{5} ni yagona kasrga aylantiring.

$$\frac{81}{16}a^{12}b^{8}\times \left(\frac{a^{2}a^{2}b^{5}}{3}\right)^{3}$$

\frac{a^{2}a^{2}b^{5}}{3}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{81}{16}a^{12}b^{8}\times \frac{\left(a^{2}a^{2}b^{5}\right)^{3}}{3^{3}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{81}{16} ni \frac{\left(a^{2}a^{2}b^{5}\right)^{3}}{3^{3}} ga ko‘paytiring.

$$\frac{81\left(a^{2}a^{2}b^{5}\right)^{3}}{16\times 3^{3}}a^{12}b^{8}$$

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

$$\frac{81\left(a^{4}b^{5}\right)^{3}}{16\times 3^{3}}a^{12}b^{8}$$

\left(a^{4}b^{5}\right)^{3} ni kengaytirish.

$$\frac{81\left(a^{4}\right)^{3}\left(b^{5}\right)^{3}}{16\times 3^{3}}a^{12}b^{8}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va 3 ni ko‘paytirib, 12 ni oling.

$$\frac{81a^{12}\left(b^{5}\right)^{3}}{16\times 3^{3}}a^{12}b^{8}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 5 va 3 ni ko‘paytirib, 15 ni oling.

$$\frac{81a^{12}b^{15}}{16\times 3^{3}}a^{12}b^{8}$$

3 daraja ko‘rsatkichini 3 ga hisoblang va 27 ni qiymatni oling.

$$\frac{81a^{12}b^{15}}{16\times 27}a^{12}b^{8}$$

432 hosil qilish uchun 16 va 27 ni ko'paytirish.

$$\frac{81a^{12}b^{15}}{432}a^{12}b^{8}$$

\frac{3}{16}a^{12}b^{15} ni olish uchun 81a^{12}b^{15} ni 432 ga bo‘ling.

$$\frac{3}{16}a^{12}b^{15}a^{12}b^{8}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 12 va 12 ni qo‘shib, 24 ni oling.

$$\frac{3}{16}a^{24}b^{15}b^{8}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 15 va 8 ni qo‘shib, 23 ni oling.

$$\frac{3}{16}a^{24}b^{23}$$

Kengaytirish

$$\frac{3b^{23}a^{24}}{16}$$

Yechim qadamlari

\left(-\frac{3}{2}a^{3}b^{2}\right)^{4} ni kengaytirish.

$$\left(-\frac{3}{2}\right)^{4}\left(a^{3}\right)^{4}\left(b^{2}\right)^{4}\times \left(\frac{a^{2}}{3}a^{2}b^{5}\right)^{3}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 4 ni ko‘paytirib, 12 ni oling.

$$\left(-\frac{3}{2}\right)^{4}a^{12}\left(b^{2}\right)^{4}\times \left(\frac{a^{2}}{3}a^{2}b^{5}\right)^{3}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 4 ni ko‘paytirib, 8 ni oling.

$$\left(-\frac{3}{2}\right)^{4}a^{12}b^{8}\times \left(\frac{a^{2}}{3}a^{2}b^{5}\right)^{3}$$

4 daraja ko‘rsatkichini -\frac{3}{2} ga hisoblang va \frac{81}{16} ni qiymatni oling.

$$\frac{81}{16}a^{12}b^{8}\times \left(\frac{a^{2}}{3}a^{2}b^{5}\right)^{3}$$

\frac{a^{2}}{3}a^{2} ni yagona kasrga aylantiring.

$$\frac{81}{16}a^{12}b^{8}\times \left(\frac{a^{2}a^{2}}{3}b^{5}\right)^{3}$$

\frac{a^{2}a^{2}}{3}b^{5} ni yagona kasrga aylantiring.

$$\frac{81}{16}a^{12}b^{8}\times \left(\frac{a^{2}a^{2}b^{5}}{3}\right)^{3}$$

\frac{a^{2}a^{2}b^{5}}{3}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{81}{16}a^{12}b^{8}\times \frac{\left(a^{2}a^{2}b^{5}\right)^{3}}{3^{3}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{81}{16} ni \frac{\left(a^{2}a^{2}b^{5}\right)^{3}}{3^{3}} ga ko‘paytiring.

$$\frac{81\left(a^{2}a^{2}b^{5}\right)^{3}}{16\times 3^{3}}a^{12}b^{8}$$

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

$$\frac{81\left(a^{4}b^{5}\right)^{3}}{16\times 3^{3}}a^{12}b^{8}$$

\left(a^{4}b^{5}\right)^{3} ni kengaytirish.

$$\frac{81\left(a^{4}\right)^{3}\left(b^{5}\right)^{3}}{16\times 3^{3}}a^{12}b^{8}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va 3 ni ko‘paytirib, 12 ni oling.

$$\frac{81a^{12}\left(b^{5}\right)^{3}}{16\times 3^{3}}a^{12}b^{8}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 5 va 3 ni ko‘paytirib, 15 ni oling.

$$\frac{81a^{12}b^{15}}{16\times 3^{3}}a^{12}b^{8}$$

3 daraja ko‘rsatkichini 3 ga hisoblang va 27 ni qiymatni oling.

$$\frac{81a^{12}b^{15}}{16\times 27}a^{12}b^{8}$$

432 hosil qilish uchun 16 va 27 ni ko'paytirish.

$$\frac{81a^{12}b^{15}}{432}a^{12}b^{8}$$

\frac{3}{16}a^{12}b^{15} ni olish uchun 81a^{12}b^{15} ni 432 ga bo‘ling.

$$\frac{3}{16}a^{12}b^{15}a^{12}b^{8}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 12 va 12 ni qo‘shib, 24 ni oling.

$$\frac{3}{16}a^{24}b^{15}b^{8}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 15 va 8 ni qo‘shib, 23 ni oling.

$$\frac{3}{16}a^{24}b^{23}$$