15p^12/5p^8 eching

$$\frac { 15 p ^ { 12 } } { 5 p ^ { 8 } }$$

Baholash

$$3p^{4}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(15p^{12}\right)^{1}\times \frac{1}{5p^{8}}$$

Ikki yoki undan ko'p raqam koʻpaytmasini daraja ko'rsatkichiga oshirish uchun har bir raqamni daraja ko'rsatkichiga oshiring va ularning koʻpaytmasini chiqaring.

$$15^{1}\left(p^{12}\right)^{1}\times \frac{1}{5}\times \frac{1}{p^{8}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$15^{1}\times \frac{1}{5}\left(p^{12}\right)^{1}\times \frac{1}{p^{8}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring.

$$15^{1}\times \frac{1}{5}p^{12}p^{8\left(-1\right)}$$

8 ni -1 marotabaga ko'paytirish.

$$15^{1}\times \frac{1}{5}p^{12}p^{-8}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$15^{1}\times \frac{1}{5}p^{12-8}$$

12 va -8 belgilarini qo'shish.

$$15^{1}\times \frac{1}{5}p^{4}$$

15 ni 1 daraja ko'rsatgichiga oshirish.

$$15\times \frac{1}{5}p^{4}$$

15 ni \frac{1}{5} marotabaga ko'paytirish.

$$3p^{4}$$

Eksponent koeffitsienti uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{15^{1}p^{12}}{5^{1}p^{8}}$$

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\frac{15^{1}p^{12-8}}{5^{1}}$$

12 dan 8 ni ayirish.

$$\frac{15^{1}p^{4}}{5^{1}}$$

15 ni 5 ga bo'lish.

$$3p^{4}$$

p ga nisbatan hosilani topish

$$12p^{3}$$

Yechim qadamlari

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{15}{5}p^{12-8})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}p}(3p^{4})$$

Polinomialning hosilasi bu uning shartlari hosilasining yig‘indisiga teng. Konstant shartning hosilasi 0. ax^{n} ning hosilasi nax^{n-1}.

$$4\times 3p^{4-1}$$

Arifmetik hisobni amalga oshirish.

$$12p^{3}$$