what is the quotient $\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}$ in simplified form? assume $p\neq0,q\neq0$.\n$…

what is the quotient $\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}$ in simplified form? assume $p\neq0,q\neq0$.\n$-\frac{3p^{8}}{4q^{3}}$\n$-\frac{3}{4p^{16}q^{9}}$\n$-\frac{p^{8}}{5q^{3}}$\n$-\frac{1}{5p^{16}q^{9}}$

what is the quotient $\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}$ in simplified form? assume $p\neq0,q\neq0$.\n$-\frac{3p^{8}}{4q^{3}}$\n$-\frac{3}{4p^{16}q^{9}}$\n$-\frac{p^{8}}{5q^{3}}$\n$-\frac{1}{5p^{16}q^{9}}$

Answer

Explanation:

Step1: Simplify the coefficient

Divide 15 by - 20: $\frac{15}{-20}=-\frac{3}{4}$.

Step2: Use the quotient - rule of exponents for $p$ terms

For $p$ terms, $\frac{p^{-4}}{p^{-12}}=p^{-4-(-12)} = p^{8}$ (since $\frac{a^{m}}{a^{n}}=a^{m - n}$).

Step3: Use the quotient - rule of exponents for $q$ terms

For $q$ terms, $\frac{q^{-6}}{q^{-3}}=q^{-6-(-3)}=q^{-3}=\frac{1}{q^{3}}$ (since $\frac{a^{m}}{a^{n}}=a^{m - n}$).

Step4: Combine the results

Multiply the simplified coefficient and the simplified variable terms: $-\frac{3}{4}\times p^{8}\times\frac{1}{q^{3}}=-\frac{3p^{8}}{4q^{3}}$.

Answer:

$-\frac{3p^{8}}{4q^{3}}$