Question

use the quotient rule for exponents to simplify.
\\(\frac{-35p^{7}q^{12}r^{8}}{7pq^{5}r^{4}}\\)
\\(\frac{-35p^{7}q^{12}r^{8}}{7pq^{5}r^{4}} = \square\\)
(simplify your answer. type your answer using exponential notation. use positive exponents only.)

Explanation:

Step1: Simplify the coefficient

Divide the coefficient \(-35\) by \(7\).
\(\frac{-35}{7} = -5\)

Step2: Simplify the \(p\) terms using quotient rule

The quotient rule for exponents is \(\frac{a^m}{a^n}=a^{m - n}\). For the \(p\) terms, we have \(\frac{p^7}{p^1}=p^{7 - 1}=p^6\) (since \(p = p^1\))

Step3: Simplify the \(q\) terms using quotient rule

For the \(q\) terms, \(\frac{q^{12}}{q^5}=q^{12 - 5}=q^7\)

Step4: Simplify the \(r\) terms using quotient rule

For the \(r\) terms, \(\frac{r^8}{r^4}=r^{8 - 4}=r^4\)

Step5: Combine all the simplified terms

Multiply the coefficient and the simplified variable terms together: \(-5\times p^6\times q^7\times r^4=-5p^6q^7r^4\)

Answer:

\(-5p^{6}q^{7}r^{4}\)