(3a^{2})^{3}:(-1/3a)^{5}-a(a^{12}:a^7)+(-9)^4a+(-5a^3)^2 eching

$$( 3 a ^ { 2 } ) ^ { 3 } : ( - \frac { 1 } { 3 } a ) ^ { 5 } - a ( a ^ { 12 } : a ^ { 7 } ) + ( - 9 ) ^ { 4 } a + ( - 5 a ^ { 3 } ) ^ { 2 }$$

Baholash

$$24a^{6}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 12 dan 7 ni ayirib, 5 ni oling.

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

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 5 ni qo‘shib, 6 ni oling.

$$\frac{\left(3a^{2}\right)^{3}}{\left(-\frac{1}{3}a\right)^{5}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

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

$$\frac{3^{3}\left(a^{2}\right)^{3}}{\left(-\frac{1}{3}a\right)^{5}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

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

$$\frac{3^{3}a^{6}}{\left(-\frac{1}{3}a\right)^{5}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

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

$$\frac{27a^{6}}{\left(-\frac{1}{3}a\right)^{5}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

\left(-\frac{1}{3}a\right)^{5} ni kengaytirish.

$$\frac{27a^{6}}{\left(-\frac{1}{3}\right)^{5}a^{5}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

5 daraja ko‘rsatkichini -\frac{1}{3} ga hisoblang va -\frac{1}{243} ni qiymatni oling.

$$\frac{27a^{6}}{-\frac{1}{243}a^{5}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

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

$$\frac{27a}{-\frac{1}{243}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

27a ni -\frac{1}{243} ga bo'lish 27a ga k'paytirish -\frac{1}{243} ga qaytarish.

$$\frac{27a\times 243}{-1}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

6561 hosil qilish uchun 27 va 243 ni ko'paytirish.

$$\frac{6561a}{-1}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

Istalgan sonni -1 ga boʻlsangiz, uning qarama-qarshisi chiqadi.

$$-6561a-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

4 daraja ko‘rsatkichini -9 ga hisoblang va 6561 ni qiymatni oling.

$$-6561a-a^{6}+6561a+\left(-5a^{3}\right)^{2}$$

0 ni olish uchun -6561a va 6561a ni birlashtirish.

$$-a^{6}+\left(-5a^{3}\right)^{2}$$

\left(-5a^{3}\right)^{2} ni kengaytirish.

$$-a^{6}+\left(-5\right)^{2}\left(a^{3}\right)^{2}$$

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

$$-a^{6}+\left(-5\right)^{2}a^{6}$$

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

$$-a^{6}+25a^{6}$$

24a^{6} ni olish uchun -a^{6} va 25a^{6} ni birlashtirish.

$$24a^{6}$$

Kengaytirish

$$24a^{6}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 12 dan 7 ni ayirib, 5 ni oling.

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

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 5 ni qo‘shib, 6 ni oling.

$$\frac{\left(3a^{2}\right)^{3}}{\left(-\frac{1}{3}a\right)^{5}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

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

$$\frac{3^{3}\left(a^{2}\right)^{3}}{\left(-\frac{1}{3}a\right)^{5}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

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

$$\frac{3^{3}a^{6}}{\left(-\frac{1}{3}a\right)^{5}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

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

$$\frac{27a^{6}}{\left(-\frac{1}{3}a\right)^{5}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

\left(-\frac{1}{3}a\right)^{5} ni kengaytirish.

$$\frac{27a^{6}}{\left(-\frac{1}{3}\right)^{5}a^{5}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

5 daraja ko‘rsatkichini -\frac{1}{3} ga hisoblang va -\frac{1}{243} ni qiymatni oling.

$$\frac{27a^{6}}{-\frac{1}{243}a^{5}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

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

$$\frac{27a}{-\frac{1}{243}}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

27a ni -\frac{1}{243} ga bo'lish 27a ga k'paytirish -\frac{1}{243} ga qaytarish.

$$\frac{27a\times 243}{-1}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

6561 hosil qilish uchun 27 va 243 ni ko'paytirish.

$$\frac{6561a}{-1}-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

Istalgan sonni -1 ga boʻlsangiz, uning qarama-qarshisi chiqadi.

$$-6561a-a^{6}+\left(-9\right)^{4}a+\left(-5a^{3}\right)^{2}$$

4 daraja ko‘rsatkichini -9 ga hisoblang va 6561 ni qiymatni oling.

$$-6561a-a^{6}+6561a+\left(-5a^{3}\right)^{2}$$

0 ni olish uchun -6561a va 6561a ni birlashtirish.

$$-a^{6}+\left(-5a^{3}\right)^{2}$$

\left(-5a^{3}\right)^{2} ni kengaytirish.

$$-a^{6}+\left(-5\right)^{2}\left(a^{3}\right)^{2}$$

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

$$-a^{6}+\left(-5\right)^{2}a^{6}$$

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

$$-a^{6}+25a^{6}$$

24a^{6} ni olish uchun -a^{6} va 25a^{6} ni birlashtirish.

$$24a^{6}$$