(frac{3a^{2}c^{5}}{-4ac^6})^-2*(5a/c^3)^3 eching

$$( \frac { 3 a ^ { 2 } c ^ { 5 } } { - 4 a c ^ { 6 } } ) ^ { - 2 } \cdot ( \frac { 5 a } { c ^ { 3 } } ) ^ { 3 }$$

Baholash

$$\frac{2000a}{9c^{7}}$$

Yechim qadamlari

Surat va maxrajdagi ikkala ac^{5} ni qisqartiring.

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

\frac{3a}{-4c}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

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

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\left(3a\right)^{-2}}{\left(-4c\right)^{-2}} ni \frac{\left(5a\right)^{3}}{\left(c^{3}\right)^{3}} ga ko‘paytiring.

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 3 ni ko‘paytirib, 9 ni oling.

$$\frac{\left(3a\right)^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}c^{9}}$$

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

$$\frac{3^{-2}a^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}c^{9}}$$

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

$$\frac{\frac{1}{9}a^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}c^{9}}$$

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

$$\frac{\frac{1}{9}a^{-2}\times 5^{3}a^{3}}{\left(-4c\right)^{-2}c^{9}}$$

3 daraja ko‘rsatkichini 5 ga hisoblang va 125 ni qiymatni oling.

$$\frac{\frac{1}{9}a^{-2}\times 125a^{3}}{\left(-4c\right)^{-2}c^{9}}$$

\frac{125}{9} hosil qilish uchun \frac{1}{9} va 125 ni ko'paytirish.

$$\frac{\frac{125}{9}a^{-2}a^{3}}{\left(-4c\right)^{-2}c^{9}}$$

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

$$\frac{\frac{125}{9}a^{1}}{\left(-4c\right)^{-2}c^{9}}$$

\left(-4c\right)^{-2} ni kengaytirish.

$$\frac{\frac{125}{9}a^{1}}{\left(-4\right)^{-2}c^{-2}c^{9}}$$

-2 daraja ko‘rsatkichini -4 ga hisoblang va \frac{1}{16} ni qiymatni oling.

$$\frac{\frac{125}{9}a^{1}}{\frac{1}{16}c^{-2}c^{9}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -2 va 9 ni qo‘shib, 7 ni oling.

$$\frac{\frac{125}{9}a^{1}}{\frac{1}{16}c^{7}}$$

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

$$\frac{\frac{125}{9}a}{\frac{1}{16}c^{7}}$$

Kengaytirish

$$\frac{2000a}{9c^{7}}$$

Yechim qadamlari

Surat va maxrajdagi ikkala ac^{5} ni qisqartiring.

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

\frac{3a}{-4c}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

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

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\left(3a\right)^{-2}}{\left(-4c\right)^{-2}} ni \frac{\left(5a\right)^{3}}{\left(c^{3}\right)^{3}} ga ko‘paytiring.

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 3 ni ko‘paytirib, 9 ni oling.

$$\frac{\left(3a\right)^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}c^{9}}$$

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

$$\frac{3^{-2}a^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}c^{9}}$$

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

$$\frac{\frac{1}{9}a^{-2}\times \left(5a\right)^{3}}{\left(-4c\right)^{-2}c^{9}}$$

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

$$\frac{\frac{1}{9}a^{-2}\times 5^{3}a^{3}}{\left(-4c\right)^{-2}c^{9}}$$

3 daraja ko‘rsatkichini 5 ga hisoblang va 125 ni qiymatni oling.

$$\frac{\frac{1}{9}a^{-2}\times 125a^{3}}{\left(-4c\right)^{-2}c^{9}}$$

\frac{125}{9} hosil qilish uchun \frac{1}{9} va 125 ni ko'paytirish.

$$\frac{\frac{125}{9}a^{-2}a^{3}}{\left(-4c\right)^{-2}c^{9}}$$

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

$$\frac{\frac{125}{9}a^{1}}{\left(-4c\right)^{-2}c^{9}}$$

\left(-4c\right)^{-2} ni kengaytirish.

$$\frac{\frac{125}{9}a^{1}}{\left(-4\right)^{-2}c^{-2}c^{9}}$$

-2 daraja ko‘rsatkichini -4 ga hisoblang va \frac{1}{16} ni qiymatni oling.

$$\frac{\frac{125}{9}a^{1}}{\frac{1}{16}c^{-2}c^{9}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -2 va 9 ni qo‘shib, 7 ni oling.

$$\frac{\frac{125}{9}a^{1}}{\frac{1}{16}c^{7}}$$

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

$$\frac{\frac{125}{9}a}{\frac{1}{16}c^{7}}$$