Question

use the quotient rule to simplify the expression. assume that all bases are not equal to 0.\\(\frac{p^{7}q^{9}}{p^{2}q^{6}}\\)\\(\frac{p^{7}q^{9}}{p^{2}q^{6}} = square\\)

Explanation:

Step1: Apply quotient rule to \( p \) terms

The quotient rule for exponents is \( \frac{a^m}{a^n} = a^{m - n} \). For the \( p \) terms, \( \frac{p^7}{p^2} = p^{7 - 2} \)
\( p^{7 - 2} = p^5 \)

Step2: Apply quotient rule to \( q \) terms

For the \( q \) terms, \( \frac{q^9}{q^6} = q^{9 - 6} \)
\( q^{9 - 6} = q^3 \)

Step3: Combine the results

Multiply the simplified \( p \) and \( q \) terms together.
\( p^5 \times q^3 = p^5q^3 \)

Answer:

\( p^5q^3 \)