(2c^{3}d^{2})^{5}(frac{c^{8}d^8}{4c^2d})^3quad2^5 eching

$$( 2 c ^ { 3 } d ^ { 2 } ) ^ { 5 } ( \frac { c ^ { 8 } d ^ { 8 } } { 4 c ^ { 2 } d } ) ^ { 3 } \quad 2 ^ { 5 }$$

Baholash

$$16d^{31}c^{33}$$

Yechim qadamlari

\left(2c^{3}d^{2}\right)^{5} ni kengaytirish.

$$2^{5}\left(c^{3}\right)^{5}\left(d^{2}\right)^{5}\times \left(\frac{c^{8}d^{8}}{4c^{2}d}\right)^{3}\times 2^{5}$$

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

$$2^{5}c^{15}\left(d^{2}\right)^{5}\times \left(\frac{c^{8}d^{8}}{4c^{2}d}\right)^{3}\times 2^{5}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 5 ni ko‘paytirib, 10 ni oling.

$$2^{5}c^{15}d^{10}\times \left(\frac{c^{8}d^{8}}{4c^{2}d}\right)^{3}\times 2^{5}$$

5 daraja ko‘rsatkichini 2 ga hisoblang va 32 ni qiymatni oling.

$$32c^{15}d^{10}\times \left(\frac{c^{8}d^{8}}{4c^{2}d}\right)^{3}\times 2^{5}$$

Surat va maxrajdagi ikkala dc^{2} ni qisqartiring.

$$32c^{15}d^{10}\times \left(\frac{c^{6}d^{7}}{4}\right)^{3}\times 2^{5}$$

\frac{c^{6}d^{7}}{4}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$32c^{15}d^{10}\times \frac{\left(c^{6}d^{7}\right)^{3}}{4^{3}}\times 2^{5}$$

5 daraja ko‘rsatkichini 2 ga hisoblang va 32 ni qiymatni oling.

$$32c^{15}d^{10}\times \frac{\left(c^{6}d^{7}\right)^{3}}{4^{3}}\times 32$$

1024 hosil qilish uchun 32 va 32 ni ko'paytirish.

$$1024c^{15}d^{10}\times \frac{\left(c^{6}d^{7}\right)^{3}}{4^{3}}$$

\left(c^{6}d^{7}\right)^{3} ni kengaytirish.

$$1024c^{15}d^{10}\times \frac{\left(c^{6}\right)^{3}\left(d^{7}\right)^{3}}{4^{3}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 6 va 3 ni ko‘paytirib, 18 ni oling.

$$1024c^{15}d^{10}\times \frac{c^{18}\left(d^{7}\right)^{3}}{4^{3}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 7 va 3 ni ko‘paytirib, 21 ni oling.

$$1024c^{15}d^{10}\times \frac{c^{18}d^{21}}{4^{3}}$$

3 daraja ko‘rsatkichini 4 ga hisoblang va 64 ni qiymatni oling.

$$1024c^{15}d^{10}\times \frac{c^{18}d^{21}}{64}$$

1024 va 64 ichida eng katta umumiy 64 faktorini bekor qiling.

$$16c^{18}d^{21}c^{15}d^{10}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 18 va 15 ni qo‘shib, 33 ni oling.

$$16c^{33}d^{21}d^{10}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 21 va 10 ni qo‘shib, 31 ni oling.

$$16c^{33}d^{31}$$

Kengaytirish

$$16d^{31}c^{33}$$

Yechim qadamlari

\left(2c^{3}d^{2}\right)^{5} ni kengaytirish.

$$2^{5}\left(c^{3}\right)^{5}\left(d^{2}\right)^{5}\times \left(\frac{c^{8}d^{8}}{4c^{2}d}\right)^{3}\times 2^{5}$$

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

$$2^{5}c^{15}\left(d^{2}\right)^{5}\times \left(\frac{c^{8}d^{8}}{4c^{2}d}\right)^{3}\times 2^{5}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 5 ni ko‘paytirib, 10 ni oling.

$$2^{5}c^{15}d^{10}\times \left(\frac{c^{8}d^{8}}{4c^{2}d}\right)^{3}\times 2^{5}$$

5 daraja ko‘rsatkichini 2 ga hisoblang va 32 ni qiymatni oling.

$$32c^{15}d^{10}\times \left(\frac{c^{8}d^{8}}{4c^{2}d}\right)^{3}\times 2^{5}$$

Surat va maxrajdagi ikkala dc^{2} ni qisqartiring.

$$32c^{15}d^{10}\times \left(\frac{c^{6}d^{7}}{4}\right)^{3}\times 2^{5}$$

\frac{c^{6}d^{7}}{4}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$32c^{15}d^{10}\times \frac{\left(c^{6}d^{7}\right)^{3}}{4^{3}}\times 2^{5}$$

5 daraja ko‘rsatkichini 2 ga hisoblang va 32 ni qiymatni oling.

$$32c^{15}d^{10}\times \frac{\left(c^{6}d^{7}\right)^{3}}{4^{3}}\times 32$$

1024 hosil qilish uchun 32 va 32 ni ko'paytirish.

$$1024c^{15}d^{10}\times \frac{\left(c^{6}d^{7}\right)^{3}}{4^{3}}$$

\left(c^{6}d^{7}\right)^{3} ni kengaytirish.

$$1024c^{15}d^{10}\times \frac{\left(c^{6}\right)^{3}\left(d^{7}\right)^{3}}{4^{3}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 6 va 3 ni ko‘paytirib, 18 ni oling.

$$1024c^{15}d^{10}\times \frac{c^{18}\left(d^{7}\right)^{3}}{4^{3}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 7 va 3 ni ko‘paytirib, 21 ni oling.

$$1024c^{15}d^{10}\times \frac{c^{18}d^{21}}{4^{3}}$$

3 daraja ko‘rsatkichini 4 ga hisoblang va 64 ni qiymatni oling.

$$1024c^{15}d^{10}\times \frac{c^{18}d^{21}}{64}$$

1024 va 64 ichida eng katta umumiy 64 faktorini bekor qiling.

$$16c^{18}d^{21}c^{15}d^{10}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 18 va 15 ni qo‘shib, 33 ni oling.

$$16c^{33}d^{21}d^{10}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 21 va 10 ni qo‘shib, 31 ni oling.

$$16c^{33}d^{31}$$