Question

Simplify the expression.
`- 5 {w}^(4) {y}^( - 2) / - 15 {w}^( - 6) {y}^(2)`w≠0, y≠0

Answer 1

Question:

Simplify the expression

`(-5w^4y^(-2))/(-15w^(-6)y^2),w\\e0,y\\e0`

Step 1:Apply the fraction rule

`\begin{gathered} (-a)/(-b)=(a)/(b) \\ (-5)/(-15)=(1)/(3) \end{gathered}`
`(-5w^4y^(-2))/(-15w^(-6)y^2)=(w^4y^(-2))/(3w^(-6)y^2)`

Step 2:Apply the law of indices

`(a^m)/(a^n)=a^(m-n)`
`(w^4y^(-2))/(3w^(-6)y^2)=(w^(4-(-6))y^(-2-2))/(3)`
`\begin{gathered} (w^(4-(-6))y^(-2-2))/(3) \\ =(w^(4+6)y^(-4))/(3) \\ =(w^(10)y^(-4))/(3) \end{gathered}`

Step 3: Apply the fractional exponent of indices

`a^(-m)=(1)/(a^m)`
`\begin{gathered} (w^(10)y^(-4))/(3) \\ =(w^(10))/(3)*(1)/(y^4) \\ =(w^(10))/(3y^4) \end{gathered}`

Hence,

The final answer = w¹⁰/3y⁴