Question

8 multiple answer 1 point choose all expressions that are equivalent to: ((6xy)^{\frac{1}{3}}) (sqrt3{2xy}) (sqrt3{6xy}) (6sqrt3{xy}) (2sqrt3{xy})

Explanation:

Step1: Recall exponent-root rule

The rule states $a^{\frac{1}{n}} = \sqrt[n]{a}$

Step2: Apply rule to given expression

$(6xy)^{\frac{1}{3}} = \sqrt[3]{6xy}$

Step3: Compare with options

Check each option against the simplified form:

• $\sqrt[3]{2xy}$: Incorrect, radicand does not match.
• $\sqrt[3]{6xy}$: Correct, matches the simplified form.
• $6\sqrt[3]{xy}$: Incorrect, this equals $6(xy)^{\frac{1}{3}}

eq (6xy)^{\frac{1}{3}}$.

• $2\sqrt[3]{xy}$: Incorrect, this equals $2(xy)^{\frac{1}{3}}

eq (6xy)^{\frac{1}{3}}$.

Answer:

$\boldsymbol{\sqrt[3]{6xy}}$