Question

value: 2
simplify
$left(x^{\frac{2}{3}} y^{\frac{1}{3}}
ight)^{\frac{1}{4}}$
\bigcirc a. $(xy)^{\frac{1}{4}}$
\bigcirc b. $x^{\frac{1}{6}} y^{\frac{1}{12}}$
\bigcirc c. $x^{\frac{3}{4}} y^{\frac{7}{12}}$
\bigcirc d. $x^{\frac{3}{7}} y^{\frac{2}{7}}$

Explanation:

Step1: Apply power of a product rule

$(x^{\frac{2}{3}}y^{\frac{1}{3}})^{\frac{1}{4}} = (x^{\frac{2}{3}})^{\frac{1}{4}} \cdot (y^{\frac{1}{3}})^{\frac{1}{4}}$

Step2: Apply power of a power rule

$x^{\frac{2}{3} \times \frac{1}{4}} \cdot y^{\frac{1}{3} \times \frac{1}{4}}$

Step3: Calculate exponents

$x^{\frac{2}{12}} \cdot y^{\frac{1}{12}} = x^{\frac{1}{6}}y^{\frac{1}{12}}$

Answer:

b. $x^{\frac{1}{6}} y^{\frac{1}{12}}$