Problem

Simplify.
\[
\left(\frac{-2 y}{x^{3}}\right)^{5}
\]
Write your answer without parentheses.

Answer

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Answer

Final Answer: \(\boxed{-32 y^{5} x^{-15}}\)

Steps

Step 1 :The given expression is a power of a fraction. To simplify it, we can apply the power to both the numerator and the denominator separately.

Step 2 :The power of a product is the product of the powers, so we can apply the power to each factor in the numerator and denominator separately.

Step 3 :The power of a negative number is negative if the power is odd, and positive if the power is even. In this case, the power is 5, which is odd, so the result will be negative.

Step 4 :The power of a variable is the product of the power and the exponent of the variable. In this case, the variable is x with an exponent of 3, and the power is 5, so the new exponent of x will be 3*5=15.

Step 5 :Substituting the values, we get the expression as \(-32*y^{5}/x^{15}\).

Step 6 :Final Answer: \(\boxed{-32 y^{5} x^{-15}}\)

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