(15p^6)div(5p^-3) eching

$$( 15 p ^ { 6 } ) \div ( 5 p ^ { - 3 } )$$

Baholash

$$3p^{9}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(15p^{6}\right)^{1}\times \frac{1}{5p^{-3}}$$

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

$$15^{1}\left(p^{6}\right)^{1}\times \frac{1}{5}\times \frac{1}{p^{-3}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$15^{1}\times \frac{1}{5}\left(p^{6}\right)^{1}\times \frac{1}{p^{-3}}$$

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

$$15^{1}\times \frac{1}{5}p^{6}p^{-3\left(-1\right)}$$

-3 ni -1 marotabaga ko'paytirish.

$$15^{1}\times \frac{1}{5}p^{6}p^{3}$$

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

$$15^{1}\times \frac{1}{5}p^{6+3}$$

6 va 3 belgilarini qo'shish.

$$15^{1}\times \frac{1}{5}p^{9}$$

15 ni 1 daraja ko'rsatgichiga oshirish.

$$15\times \frac{1}{5}p^{9}$$

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

$$3p^{9}$$

p ga nisbatan hosilani topish

$$27p^{8}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{15}{5}p^{6-\left(-3\right)})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}p}(3p^{9})$$

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

$$9\times 3p^{9-1}$$

Arifmetik hisobni amalga oshirish.

$$27p^{8}$$