Question

question 2 of 5

select the correct answer.

which expression is equivalent to \\(\sqrt3{x^{10}}\\) if \\(x \
eq 0\\)?

\\(x^7\\)

\\(x^3\sqrt{x^7}\\)

\\(x^5\\)

\\(x^3\sqrt3{x}\\)

Explanation:

Convert the radical expression to rational exponent form

$$ \sqrt[3]{x^{10}} = (x^{10})^{\frac{1}{3}} = x^{\frac{10}{3}} $$

Decompose the rational exponent into integer and fractional parts

$$ x^{\frac{10}{3}} = x^{3 + \frac{1}{3}} = x^3 \cdot x^{\frac{1}{3}} $$

Convert back to radical form

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

Answer:

• (A) \(x^7\)
• (B) \(x^3\sqrt{x^7}\)
• (C) \(x^5\)
• (D) \(x^3\sqrt[3]{x}\) (Correct answer)