Select the equivalent expression. (x^(-3)x^(2)y^(7))/(y^(6)) (x)/(y) (y)/(x) x^(5)y (1)/(x^(5)y)

Simplify x terms: To find the equivalent expression, we need to simplify the given expression using the properties of exponents.Simplify y terms: First, we simplify the x terms by adding the exponents since they have the same base and are being multiplied. x^(-3) * x^(2) = x^(-3 + 2) = x^(-1).Combine x and y terms: Next, we simplify the y terms by subtracting the exponents since y^(7) is being divided by y^(6). y^(7) / y^(6) = y^(7 - 6) = y^(1) = y.Final equivalent expression: Now we combine the simplified x and y terms. (x^(-1)) * y = (1/x) * y.The expression (1/x) * y is equivalent to y/x. Therefore, the equivalent expression is y/x.

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Q. Select the equivalent expression.

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\frac{x^{-3} x^{2} y^{7}}{y^{6}}

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\frac{x}{y}

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\frac{y}{x}

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x^{5} y

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\frac{1}{x^{5} y}

Simplify $x$ terms: To find the equivalent expression, we need to simplify the given expression using the properties of exponents.
Simplify $y$ terms: First, we simplify the $x$ terms by adding the exponents since they have the same base and are being multiplied. $x^{(-3)} \times x^{(2)} = x^{(-3 + 2)} = x^{(-1)}.$
Combine $x$ and $y$ terms: Next, we simplify the $y$ terms by subtracting the exponents since $y^{7}$ is being divided by $y^{6}$ . $\frac{y^{7}}{y^{6}} = y^{7 - 6} = y^{1} = y$ .
Final equivalent expression: Now we combine the simplified $x$ and $y$ terms. $(x^{(-1)}) \cdot y = \left(\frac{1}{x}\right) \cdot y.$
Final equivalent expression: Now we combine the simplified $x$ and $y$ terms. $(x^{(-1)}) \cdot y = (\frac{1}{x}) \cdot y$ .The expression $(\frac{1}{x}) \cdot y$ is equivalent to $\frac{y}{x}$ .Therefore, the equivalent expression is $\frac{y}{x}$ .