Given xgt 0 and ygt 0 select the expression that is equivalent to sqrt [3](-64x^12y^4) Answer Attemptiout of 3 -4x^(1)/(4)y^(3)/(4) 4ix^(1)/(4)y^(3)/(4) -4x^4y^(4)/(3) 4ix^4y^(4)/(3)

To simplify the expression $$\sqrt [3]{-64x^{12}y^{4}}$$ , we can use the properties of exponents and radicals.

First, let's rewrite the expression inside the cube root:
$$-64x^{12}y^{4} = (-1) \cdot 64 \cdot x^{12} \cdot y^{4}$$

Now, we can apply the cube root to each factor separately:
$$\sqrt [3]{-64x^{12}y^{4}} = \sqrt [3]{-1} \cdot \sqrt [3]{64} \cdot \sqrt [3]{x^{12}} \cdot \sqrt [3]{y^{4}}$$

Simplifying each term, we have:
$$\sqrt [3]{-1} = -1$$
$$\sqrt [3]{64} = 4$$
$$\sqrt [3]{x^{12}} = x^{4}$$
$$\sqrt [3]{y^{4}} = y^{\frac {4}{3}}$$

Putting it all together, we get:
$$\sqrt [3]{-64x^{12}y^{4}} = -1 \cdot 4 \cdot x^{4} \cdot y^{\frac {4}{3}} = -4x^{4}y^{\frac {4}{3}}$$

Therefore, the expression equivalent to $$\sqrt [3]{-64x^{12}y^{4}}$$ is $$-4x^{4}y^{\frac {4}{3}}$$ .