Question

simplify the expression and write the answer with positive exponents:
\\(\frac{p^{-4}q^{2}}{p^{2}q^{-3}}\\)

select one:
\\(\bigcirc\\) a. \\(\frac{q}{p^{2}}\\)
\\(\bigcirc\\) b. \\(\frac{p^{6}}{q^{5}}\\)
\\(\bigcirc\\) c. \\(\frac{q^{5}}{p^{6}}\\)
\\(\bigcirc\\) d. \\(\frac{q^{6}}{q^{8}}\\)

Explanation:

Step1: Separate like bases

$\frac{p^{-4}}{p^2} \times \frac{q^2}{q^{-3}}$

Step2: Simplify $p$-terms (subtract exponents)

$p^{-4-2} = p^{-6} = \frac{1}{p^6}$

Step3: Simplify $q$-terms (subtract exponents)

$q^{2-(-3)} = q^{2+3} = q^5$

Step4: Combine simplified terms

$\frac{1}{p^6} \times q^5 = \frac{q^5}{p^6}$

Answer:

C. $\frac{q^5}{p^6}$