Question

multiply: \\(\sqrt6{x} \cdot \sqrt4{y^3}\\)

rewrite the expression using rational exponents with a common denominator.

• \\(xy^{\frac{11}{12}}\\)
• \\(x^{\frac{2}{12}} y^{\frac{9}{12}}\\)
• \\(x^{\frac{1}{6}} y^{\frac{3}{4}}\\)

simplify: \\(\sqrt6{x} \cdot \sqrt4{y^3}\\)

• \\(y \sqrt6{x^2}\\)
• \\(\sqrt12{x \cdot y}\\)
• \\(\sqrt12{x^2 \cdot y^9}\\)

Explanation:

Convert radicals to rational exponents

Using the Radical to Exponential Form knowledge point

$$ \sqrt[6]{x} \cdot \sqrt[4]{y^3} = x^{\frac{1}{6}} \cdot y^{\frac{3}{4}} $$

Find a common denominator

Using the Least Common Denominator knowledge point

$$
LATEXBLOCK0
$$

Rewrite with common denominator

Using the Rational Exponents knowledge point

$$ x^{\frac{1}{6}} y^{\frac{3}{4}} = x^{\frac{2}{12}} y^{\frac{9}{12}} $$

Simplify the radical product

Using the Simplifying Radical Products knowledge point

$$ x^{\frac{2}{12}} y^{\frac{9}{12}} = (x^2 y^9)^{\frac{1}{12}} = \sqrt[12]{x^2 y^9} $$

Answer:

Question 1

• (A) \(xy^{\frac{11}{12}}\)
• (B) \(x^{\frac{2}{12}} y^{\frac{9}{12}}\) (Correct answer)
• (C) \(x^{\frac{1}{6}} y^{\frac{3}{4}}\)

Question 2

• (A) \(y \sqrt[3]{x^2}\)
• (B) \(\sqrt[12]{x \cdot y}\)
• (C) \(\sqrt[12]{x^2 \cdot y^9}\) (Correct answer)