Question

6 $\frac{2x^{-3}y^{2}}{4x^{-4}y^{-1}}$

Explanation:

Step1: Simplify the coefficient

Divide 2 by 4: $\frac{2}{4}=\frac{1}{2}$

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

For $x$ terms, $\frac{x^{-3}}{x^{-4}}=x^{-3-(-4)} = x^{-3 + 4}=x^{1}=x$ according to the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$

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

For $y$ terms, $\frac{y^{2}}{y^{-1}}=y^{2-(-1)}=y^{2 + 1}=y^{3}$ according to the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$

Step4: Combine the results

Multiply the simplified coefficient and the $x$ and $y$ terms: $\frac{1}{2}xy^{3}$

Answer:

$\frac{1}{2}xy^{3}$