Question:
Simplify the expression
[tex]\frac{-5w^4y^{-2}}{-15w^{-6}y^2},w\ne0,y\ne0[/tex]
Step 1:Apply the fraction rule
[tex]\begin{gathered} \frac{-a}{-b}=\frac{a}{b} \\ \frac{-5}{-15}=\frac{1}{3} \end{gathered}[/tex][tex]\frac{-5w^4y^{-2}}{-15w^{-6}y^2}=\frac{w^4y^{-2}}{3w^{-6}y^2}[/tex]
Step 2:Apply the law of indices
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex][tex]\frac{w^4y^{-2}}{3w^{-6}y^2}=\frac{w^{4-(-6)}y^{-2-2}}{3}[/tex][tex]\begin{gathered} \frac{w^{4-(-6)}y^{-2-2}}{3} \\ =\frac{w^{4+6}y^{-4}}{3} \\ =\frac{w^{10}y^{-4}}{3} \end{gathered}[/tex]
Step 3: Apply the fractional exponent of indices
[tex]a^{-m}=\frac{1}{a^m}[/tex][tex]\begin{gathered} \frac{w^{10}y^{-4}}{3} \\ =\frac{w^{10}}{3}\times\frac{1}{y^4} \\ =\frac{w^{10}}{3y^4} \end{gathered}[/tex]
Hence,
The final answer = w¹⁰/3y⁴
