Question

what is the simplest form of \frac{\sqrt3{81x^{10}}}{\sqrt3{3x}}?

• \\(3x\\)
• \\(3x^3\\)
• \\(3x^4\sqrt{3x}\\)
• \\(3x^3\sqrt3{x^2}\\)

Explanation:

Apply the quotient property of radicals

Using the Quotient Property of Radicals knowledge point

$$ \frac{\sqrt[3]{81x^{10}}}{\sqrt[3]{3x}} = \sqrt[3]{\frac{81x^{10}}{3x}} $$

Simplify the radicand

Using the Exponent Rules knowledge point

$$ \frac{81x^{10}}{3x} = 27x^9 $$

Simplify the cube root

Using the Simplifying Cube Roots knowledge point

$$ \sqrt[3]{27x^9} = \sqrt[3]{3^3 \cdot (x^3)^3} = 3x^3 $$

Answer:

• (A) \(3x\)
• (B) \(3x^3\) (Correct answer)
• (C) \(3x^4\sqrt{3x}\)
• (D) \(3x^3\sqrt[3]{x^2}\)