Given x > 0 and y > 0, select the expression that is equivalent to root(3)(-64x^(12)y^(9)) 4ix^(4)y^(3) 4ix^(9)y^(6) -4x^(9)y^(6) -4x^(4)y^(3)

Simplify Constant Term: Simplify the cube root of the constant term. The cube root of -64 is -4 because (-4)^3 = -64.Simplify Variable Term x^(12): Simplify the cube root of the variable term x^(12). The cube root of x^(12) is x^(12/3) because when taking the cube root, you divide the exponent by 3. So, x^(12/3) = x^4.Simplify Variable Term y^(9): Simplify the cube root of the variable term y^(9). The cube root of y^(9) is y^(9/3) because when taking the cube root, you divide the exponent by 3. So, y^(9/3) = y^3.Combine Results: Combine the results from Steps 1, 2, and 3. Combining the cube roots of the constant and variable terms, we get -4x^4y^3.Check Given Options: Determine if the result is one of the given options. The result from Step 4 is -4x^4y^3, which matches one of the given options.

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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]{-64 x^{12} y^{9}}

\newline

4 i x^{4} y^{3}

\newline

4 i x^{9} y^{6}

\newline

-4 x^{9} y^{6}

\newline

-4 x^{4} y^{3}

Simplify Constant Term: Simplify the cube root of the constant term. $\newline$ The cube root of $-64$ is $-4$ because $(-4)^3 = -64$ .
Simplify Variable Term $x^{12}$ : Simplify the cube root of the variable term $x^{12}$ . The cube root of $x^{12}$ is $x^{\frac{12}{3}}$ because when taking the cube root, you divide the exponent by $3$ . So, $x^{\frac{12}{3}} = x^4$ .
Simplify Variable Term $y^{9}$ : Simplify the cube root of the variable term $y^{9}$ . The cube root of $y^{9}$ is $y^{\frac{9}{3}}$ because when taking the cube root, you divide the exponent by $3$ . So, $y^{\frac{9}{3}} = y^{3}$ .
Combine Results: Combine the results from Steps $1$ , $2$ , and $3$ . Combining the cube roots of the constant and variable terms, we get $-4x^4y^3$ .
Check Given Options: Determine if the result is one of the given options. $\newline$ The result from Step $4$ is $-4x^4y^3$ , which matches one of the given options.