Question

1. simplify the following, writing without negative \\(3p^{5}q^{-6}\cdot 8p^{-7}q^{9}\\) \\(=\\) enter your next step here

Explanation:

Step1: Multiply coefficients and like bases

Multiply the coefficients \(3\) and \(8\), and use the product rule for exponents \(a^m \cdot a^n = a^{m + n}\) for \(p\) and \(q\) terms.
\(3p^{5}q^{-6} \cdot 8p^{-7}q^{9}=(3\times8)p^{5 + (-7)}q^{-6 + 9}\)

Step2: Simplify exponents

Calculate the exponents for \(p\) and \(q\).
\(3\times8 = 24\), \(5+(-7)=-2\), \(-6 + 9 = 3\), so we have \(24p^{-2}q^{3}\)

Step3: Remove negative exponent

Use the rule \(a^{-n}=\frac{1}{a^{n}}\) to rewrite \(p^{-2}\) as \(\frac{1}{p^{2}}\).
\(24p^{-2}q^{3}=\frac{24q^{3}}{p^{2}}\)

Answer:

\(\frac{24q^{3}}{p^{2}}\)