Question

simplify the expression. assume that the denominator does not equal zero. write any variables in alphabetical order. \\(\frac{7p^{-5}q^{4}}{35p^{-3}q^{4}}\\)

Explanation:

Step1: Simplify coefficients

Simplify the fraction of the coefficients: $\frac{7}{35}=\frac{1}{5}$.

Step2: Simplify \( p \)-terms

Use the rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \) for \( p \)-terms: \( \frac{p^{-5}}{p^{-3}}=p^{-5-(-3)}=p^{-2}=\frac{1}{p^2} \).

Step3: Simplify \( q \)-terms

Use the rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \) for \( q \)-terms: \( \frac{q^4}{q}=q^{4 - 1}=q^3 \).

Step4: Combine all parts

Multiply the simplified coefficient, \( p \)-term, and \( q \)-term: \( \frac{1}{5}\times\frac{1}{p^2}\times q^3=\frac{q^3}{5p^2} \).

Answer:

\(\boldsymbol{\frac{q^3}{5p^2}}\)