(2xy^(-2))/((x^(-1))^(-4)*y^(0))

Simplify Denominator: Simplify the denominator. We have (x^(-1))^(-4) * y^(0) in the denominator. According to the power of a power rule, (a^b)^c = a^(b*c). Also, any number raised to the power of 0 is 1. So, (x^(-1))^(-4) = x^((-1)*(-4)) = x^4 and y^(0) = 1.Rewrite Expression: Rewrite the expression with the simplified denominator. Now that we have simplified the denominator, we can rewrite the expression as: (2xy^(-2))/(x^4 * 1) Since y^(0) = 1, it does not affect the multiplication and can be omitted.Combine Like Terms: Simplify the expression by combining like terms. We have 2xy^(-2) in the numerator and x^4 in the denominator. We can simplify the expression by dividing the terms with the same base. (2xy^(-2))/x^4 = 2x^(1-4)y^(-2) = 2x^(-3)y^(-2)Rewrite with Positive Exponents: Rewrite the expression with positive exponents. Since we have negative exponents, we can rewrite them with positive exponents by taking the reciprocal of the base. 2x^(-3)y^(-2) = 2/(x^3y^2)

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$\frac{2 x y^{-2}}{\left(x^{-1}\right)^{-4} \cdot y^{0}}$

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Algebra 1

Multiplication with rational exponents

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\frac{2 x y^{-2}}{\left(x^{-1}\right)^{-4} \cdot y^{0}}

Simplify Denominator: Simplify the denominator. $\newline$ We have $(x^{-1})^{-4} \times y^{0}$ in the denominator. According to the power of a power rule, $(a^{b})^{c} = a^{b\cdot c}$ . Also, any number raised to the power of $0$ is $1$ . $\newline$ So, $(x^{-1})^{-4} = x^{(-1)\cdot(-4)} = x^{4}$ and $y^{0} = 1$ .
Rewrite Expression: Rewrite the expression with the simplified denominator. $\newline$ Now that we have simplified the denominator, we can rewrite the expression as: $\newline$ $(2xy^{-2})/(x^4 \cdot 1)$ $\newline$ Since $y^{0} = 1$ , it does not affect the multiplication and can be omitted.
Combine Like Terms: Simplify the expression by combining like terms. $\newline$ We have $2xy^{-2}$ in the numerator and $x^4$ in the denominator. We can simplify the expression by dividing the terms with the same base. $\newline$ $\frac{2xy^{-2}}{x^4} = 2x^{1-4}y^{-2} = 2x^{-3}y^{-2}$
Rewrite with Positive Exponents: Rewrite the expression with positive exponents. $\newline$ Since we have negative exponents, we can rewrite them with positive exponents by taking the reciprocal of the base. $\newline$ $2x^{-3}y^{-2} = \frac{2}{x^3y^2}$