Select the equivalent expression. (×^(6)y^(-7))/(y^(-1)) (x^(7))/(y^(6)) (x^(5))/(y^(6)) (y^(6))/(x^(7)) (y^(6))/(x^(5))

Apply Quotient Rule: To simplify the expression (x^(6)y^(-7))/(y^(-1)), we need to use the properties of exponents, specifically the quotient rule which states that when dividing like bases, you subtract the exponents.Simplify y Exponents: We apply the quotient rule to the y terms: y^(-7) / y^(-1) = y^(-7 - (-1)) = y^(-7 + 1) = y^(-6).Rewrite Expression: Now we rewrite the expression with the simplified exponent for y: (x^(6)y^(-7))/(y^(-1)) = x^(6)y^(-6).Use Reciprocal Property: Since y^(-6) is the same as 1/(y^(6)), we can rewrite the expression as: x^(6) * (1/(y^(6))) = (x^(6))/(y^(6)).Final Simplified Expression: The final simplified expression is (x^(6))/(y^(6)). This matches one of the answer choices provided.

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Find derivatives of using multiple formulae

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Q. Select the equivalent expression.

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\frac{x x^{6} y^{-7}}{y^{-1}}

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\frac{x^{7}}{y^{6}}

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\frac{x^{5}}{y^{6}}

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\frac{y^{6}}{x^{7}}

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\frac{y^{6}}{x^{5}}

Apply Quotient Rule: To simplify the expression $(x^{6}y^{-7})/(y^{-1})$ , we need to use the properties of exponents, specifically the quotient rule which states that when dividing like bases, you subtract the exponents.
Simplify y Exponents: We apply the quotient rule to the y terms: $y^{-7} / y^{-1} = y^{-7 - (-1)} = y^{-7 + 1} = y^{-6}$ .
Rewrite Expression: Now we rewrite the expression with the simplified exponent for $y$ : $\frac{x^{6}y^{-7}}{y^{-1}} = x^{6}y^{-6}$ .
Use Reciprocal Property: Since $y^{-6}$ is the same as $1/(y^{6})$ , we can rewrite the expression as: $x^{6} * (1/(y^{6})) = (x^{6})/(y^{6})$ .
Final Simplified Expression: The final simplified expression is $\frac{x^{6}}{y^{6}}$ . This matches one of the answer choices provided.