Given x > 0 and y > 0, select the expression that is equivalent to root(3)(-125x^(9)y) 5ix^((1)/(3))y^(3) -5x^(3)y^((1)/(3)) 5ix^(3)y^((1)/(3)) -5x^((1)/(3))y^(3)

Simplify Constant: Simplify the constant inside the cube root. The cube root of -125 is -5 because (-5)^3 = -125.Simplify Variable x: Simplify the variable x inside the cube root. The cube root of x^9 is x^3 because (x^3)^3 = x^(3*3) = x^9.Simplify Variable y: Simplify the variable y inside the cube root. Since y is not raised to a power that is a multiple of 3, it remains inside the cube root. Therefore, the cube root of y is y^(1/3).Combine Simplified Parts: Combine the simplified parts. Combining the results from steps 1, 2, and 3, we get the expression -5x^3y^(1/3).

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Find derivatives of using multiple formulae

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Q. Given

x>0

and

y>0

, select the expression that is equivalent to

\newline

\sqrt[3]{-125 x^{9} y}

\newline

5 i x^{\frac{1}{3}} y^{3}

\newline

-5 x^{3} y^{\frac{1}{3}}

\newline

5 i x^{3} y^{\frac{1}{3}}

\newline

-5 x^{\frac{1}{3}} y^{3}

Simplify Constant: Simplify the constant inside the cube root. $\newline$ The cube root of $-125$ is $-5$ because $(-5)^3 = -125$ .
Simplify Variable $x$ : Simplify the variable $x$ inside the cube root. The cube root of $x^9$ is $x^3$ because $(x^3)^3 = x^{(3*3)} = x^9$ .
Simplify Variable $y$ : Simplify the variable $y$ inside the cube root. Since $y$ is not raised to a power that is a multiple of $3$ , it remains inside the cube root. Therefore, the cube root of $y$ is $y^{1/3}$ .
Combine Simplified Parts: Combine the simplified parts. $\newline$ Combining the results from steps $1$ , $2$ , and $3$ , we get the expression $-5x^3y^{\frac{1}{3}}$ .