which expression is equivalent to $\frac{28p^{9}q^{-5}}{12p^{-6}q^{7}}$? assume $p\neq0,q\neq0$.\n$\frac{2}{p…

which expression is equivalent to $\frac{28p^{9}q^{-5}}{12p^{-6}q^{7}}$? assume $p\neq0,q\neq0$.\n$\frac{2}{p^{15}q^{12}}$\n$\frac{7p^{15}}{3q^{12}}$\n$\frac{2q^{12}}{p^{15}}$\n$\frac{7p^{15}q^{12}}{3}$
Answer
Explanation:
Step1: Simplify the coefficient
Divide 28 by 12: $\frac{28}{12}=\frac{7}{3}$.
Step2: Use exponent - division rule for $p$ terms
When dividing $p^m$ by $p^n$, we subtract the exponents. So, $\frac{p^{9}}{p^{- 6}}=p^{9-(-6)} = p^{9 + 6}=p^{15}$.
Step3: Use exponent - division rule for $q$ terms
$\frac{q^{-5}}{q^{7}}=q^{-5 - 7}=q^{-12}=\frac{1}{q^{12}}$.
Step4: Combine the results
The original expression $\frac{28p^{9}q^{-5}}{12p^{-6}q^{7}}$ simplifies to $\frac{7}{3}\times p^{15}\times\frac{1}{q^{12}}=\frac{7p^{15}}{3q^{12}}$.
Answer:
$\frac{7p^{15}}{3q^{12}}$