Question

4 multiple answer 1 point choose all expressions that are equivalent to: (left(125x^{9}
ight)^{\frac{1}{3}}) (sqrt3{125x^{5}}) (5x^{9}) (3x^{5}) (sqrt3{125x^{9}}) (5x^{3})

Explanation:

Step1: Rewrite exponent as root

Recall that $(a)^{\frac{1}{n}} = \sqrt[n]{a}$. So:
$$(125x^9)^{\frac{1}{3}} = \sqrt[3]{125x^9}$$

Step2: Simplify the radical

Split the radical and simplify each part:
$$\sqrt[3]{125x^9} = \sqrt[3]{125} \cdot \sqrt[3]{x^9} = 5 \cdot x^{9 \cdot \frac{1}{3}} = 5x^3$$

Answer:

$\sqrt[3]{125x^9}$, $5x^3$