root(4)((405x^(3)y^(3))/(5x^(-1)y))=

Simplify Fraction Inside Root: Simplify the fraction inside the fourth root. We have the expression root(4)((405x^(3)y^(3))/(5x^(-1)y)). First, we simplify the fraction by dividing the numerator by the denominator. (405x^(3)y^(3)) / (5x^(-1)y) = (405/5) * (x^(3) * x^(1)) * (y^(3) / y) = 81 * x^(3+1) * y^(3-1) = 81 * x^(4) * y^(2)Apply Fourth Root: Apply the fourth root to the simplified expression. Now we take the fourth root of the simplified expression. root(4)(81 * x^(4) * y^(2)) Since 81 is a perfect fourth power (3^4 = 81), and x^4 is also a perfect fourth power, we can simplify further. root(4)(81) * root(4)(x^(4)) * root(4)(y^(2)) = 3 * x * root(4)(y^(2))Check Further Simplification: Check if the expression inside the fourth root can be simplified further. The expression root(4)(y^(2)) cannot be simplified further because y^2 is not a perfect fourth power. Therefore, the final simplified expression is: 3 * x * root(4)(y^(2))

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$\sqrt[4]{\frac{405 x^{3} y^{3}}{5 x^{-1} y}}=$

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Algebra 1

Multiplication with rational exponents

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\sqrt[4]{\frac{405 x^{3} y^{3}}{5 x^{-1} y}}=

Simplify Fraction Inside Root: Simplify the fraction inside the fourth root. $\newline$ We have the expression $\sqrt[4]{\frac{405x^{3}y^{3}}{5x^{-1}y}}$ . First, we simplify the fraction by dividing the numerator by the denominator. $\newline$ $\frac{405x^{3}y^{3}}{5x^{-1}y} = \frac{405}{5} \times (x^{3} \times x^{1}) \times (y^{3} / y)$ $\newline$ $= 81 \times x^{3+1} \times y^{2-1}$ $\newline$ $= 81 \times x^{4} \times y^{2}$
Apply Fourth Root: Apply the fourth root to the simplified expression. $\newline$ Now we take the fourth root of the simplified expression. $\newline$ $\sqrt[4]{81 \times x^{4} \times y^{2}}$ $\newline$ Since $81$ is a perfect fourth power ( $3^4 = 81$ ), and $x^4$ is also a perfect fourth power, we can simplify further. $\newline$ $\sqrt[4]{81}$ $\times$ $\sqrt[4]{x^{4}}$ $\times$ $\sqrt[4]{y^{2}}$ $\newline$ = $3 \times x \times \sqrt[4]{y^{2}}$
Check Further Simplification: Check if the expression inside the fourth root can be simplified further. $\newline$ The expression $\sqrt[4]{y^{2}}$ cannot be simplified further because $y^2$ is not a perfect fourth power. Therefore, the final simplified expression is: $\newline$ $3 \times x \times \sqrt[4]{y^{2}}$