Which of the following expressions is equivalent to $(-8x^2)^{\frac{2}{3}}$

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If we seperate the items inside the parenthesis:

$$( -1 \cdot 8 \cdot x \cdot x)^{\frac{2}{3}}$$

We can take care of the 2 exponent first by doubling the terms inside the parenthesis.

$$( -1 \cdot 8 \cdot x \cdot x)^{\colorbox{aqua}{$2$}\cdot \frac{1}{3}}$$ $$( -1 \cdot -1 \cdot 8 \cdot 8 \cdot x \cdot x \cdot x \cdot x)^{\frac{1}{3}}$$

The negative values cancel each other out. The current exponent is equivalent to a cube root.

$$\sqrt[3]{8\cdot 8\cdot x\cdot x \cdot x \cdot x}$$

We can take out a $x$ since there are three of them, but we should obtain the prime factors of $8$ to see if anything else can be simplified.

$$\sqrt[3]{\colorbox{aqua}{$2 \cdot 2 \cdot 2$} \cdot \colorbox{aqua}{$2 \cdot 2 \cdot 2$} \cdot \colorbox{aqua}{$x \cdot x \cdot x$} \cdot x}$$ $$= 2\cdot 2\cdot x \cdot \sqrt[3]{x}$$ $$= 4x \sqrt[3]{x}$$