To simplify the expression \((-3w^5x^{-3}y/y^3w^{-1})^{-3}\), we can follow these steps:
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Simplify the fraction inside the parentheses: \[ -3w^5x^{-3}y/y^3w^{-1} = -3 \cdot w^5 \cdot x^{-3} \cdot \frac{y}{y^3} \cdot w^{1} \] This simplifies to: \[ -3w^5x^{-3} \cdot w^{1} \cdot y^{1-3} = -3w^{5+1}x^{-3}y^{-2} = -3w^6x^{-3}y^{-2} \]
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Rewrite the expression: Now we have: \[ (-3w^6x^{-3}y^{-2})^{-3} \]
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Apply the exponent to each term inside the parentheses: \[ (-3)^{-3} \cdot (w^6)^{-3} \cdot (x^{-3})^{-3} \cdot (y^{-2})^{-3} \] Simplifying each part:
- \((-3)^{-3} = -\frac{1}{27}\)
- \((w^6)^{-3} = w^{-18}\)
- \((x^{-3})^{-3} = x^{9}\)
- \((y^{-2})^{-3} = y^{6}\)
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Combine the results: Putting it all together: \[ -\frac{1}{27} \cdot w^{-18} \cdot x^{9} \cdot y^{6} = -\frac{x^{9}y^{6}}{27w^{18}} \]
Thus, the final simplified expression is: \[ \boxed{-\frac{x^{9}y^{6}}{27w^{18}}} \]