Given x > 0 and y > 0, select the expression that is equivalent to root(3)(-125x^(14)y^(12)) 5ix^(11)y^(9) 5ix^((14)/(3))y^(4) -5x^((14)/(3))y^(4) -5x^(11)y^(9)

Evaluate Constant Term Cube Root: Evaluate the cube root of the constant term. The cube root of -125 is -5 because $(-5)^3 = -125$.Evaluate x Exponent Cube Root: Evaluate the cube root of $x^{14}$. To find the cube root of $x^{14}$, we divide the exponent by 3: $x^{(14/3)}$.Evaluate y Exponent Cube Root: Evaluate the cube root of $y^{12}$. To find the cube root of $y^{12}$, we divide the exponent by 3: $y^{(12/3)} = y^4$.Combine Results: Combine the results from Steps 1, 2, and 3. The expression equivalent to $ \sqrt[3]{-125x^{14}y^{12}} $ is $-5x^{(14/3)}y^4$.

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Calculus

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^{14} y^{12}}

\newline

5 i x^{11} y^{9}

\newline

5 i x^{\frac{14}{3}} y^{4}

\newline

-5 x^{\frac{14}{3}} y^{4}

\newline

-5 x^{11} y^{9}

Evaluate Constant Term Cube Root: Evaluate the cube root of the constant term. $\newline$ The cube root of $-125$ is $-5$ because $(-5)^3 = -125$ .
Evaluate x Exponent Cube Root: Evaluate the cube root of $x^{14}$ . $\newline$ To find the cube root of $x^{14}$ , we divide the exponent by $3$ : $x^{(14/3)}$ .
Evaluate y Exponent Cube Root: Evaluate the cube root of $y^{12}$ . $\newline$ To find the cube root of $y^{12}$ , we divide the exponent by $3$ : $y^{(12/3)} = y^4$ .
Combine Results: Combine the results from Steps $1$ , $2$ , and $3$ . $\newline$ The expression equivalent to $\sqrt[3]{-125x^{14}y^{12}}$ is $-5x^{(14/3)}y^4$ .