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

Simplify the expression.- 5 {w}^(4) {y}^( - 2) / - 15 {w}^( - 6) {y}^(2)w≠0, y≠0-example-1
User Hakunamatata
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1 Answer

22 votes
22 votes

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

User Mellifluous
by
3.2k points
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