Given x > 0 and y > 0, select the expression that is equivalent to root(3)(-64x^(9)y^(10)) 4ix^((1)/(3))y^((3)/(10)) -4x^((1)/(3))y^((3)/(10)) 4ix^(3)y^((10)/(3)) -4x^(3)y^((10)/(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: Simplify the cube root of the variable term x^(9). The cube root of x^(9) is x^(9/3) because when taking the cube root, you divide the exponent by 3. So, x^(9/3) = x^3.Simplify Variable Term y: Simplify the cube root of the variable term y^(10). The cube root of y^(10) is y^(10/3) because when taking the cube root, you divide the exponent by 3. So, y^(10/3) = y^(10/3).Combine Results: Combine the results from Steps 1, 2, and 3. Combining the results, we get the expression -4x^3y^(10/3).Check Answer Choices: Check the answer choices to find the equivalent expression. The correct expression that matches our result is -4x^(3)y^((10)/(3)).

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Given
x > 0 and
y > 0, select the expression that is equivalent to

root(3)(-64x^(9)y^(10))

4ix^((1)/(3))y^((3)/(10))

-4x^((1)/(3))y^((3)/(10))

4ix^(3)y^((10)/(3))

-4x^(3)y^((10)/(3))

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt[3]{-64 x^{9} y^{10}}$ $\newline$ $4 i x^{\frac{1}{3}} y^{\frac{3}{10}}$ $\newline$ $-4 x^{\frac{1}{3}} y^{\frac{3}{10}}$ $\newline$ $4 i x^{3} y^{\frac{10}{3}}$ $\newline$ $-4 x^{3} y^{\frac{10}{3}}$

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Math Problems

Calculus

Find derivatives of using multiple formulae

Full solution

Q. Given

x>0

and

y>0

, select the expression that is equivalent to

\newline

\sqrt[3]{-64 x^{9} y^{10}}

\newline

4 i x^{\frac{1}{3}} y^{\frac{3}{10}}

\newline

-4 x^{\frac{1}{3}} y^{\frac{3}{10}}

\newline

4 i x^{3} y^{\frac{10}{3}}

\newline

-4 x^{3} y^{\frac{10}{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 $x$ : Simplify the cube root of the variable term $x^{9}$ . The cube root of $x^{9}$ is $x^{\frac{9}{3}}$ because when taking the cube root, you divide the exponent by $3$ . So, $x^{\frac{9}{3}} = x^{3}$ .
Simplify Variable Term $y$ : Simplify the cube root of the variable term $y^{10}$ . $\newline$ The cube root of $y^{10}$ is $y^{\frac{10}{3}}$ because when taking the cube root, you divide the exponent by $3$ . So, $y^{\frac{10}{3}} = y^{\frac{10}{3}}$ .
Combine Results: Combine the results from Steps $1$ , $2$ , and $3$ . Combining the results, we get the expression $-4x^3y^{(10/3)}$ .
Check Answer Choices: Check the answer choices to find the equivalent expression. $\newline$ The correct expression that matches our result is $-4x^{3}y^{\left(\frac{10}{3}\right)}$ .