Question

the volume of a cube is \\(27n^{27}\\) cubic units. what is the length of one side of the cube?

\\(3n^3\\) units
\\(3n^9\\) units
\\(27n^3\\) units
\\(27n^9\\) units

Explanation:

Set up the volume equation

$$ V = s^3 = 27n^{27} $$

Solve for the side length

$$ s = \sqrt[3]{27n^{27}} $$

Simplify the radical expression

$$ s = \sqrt[3]{27} \cdot \sqrt[3]{n^{27}} = 3 \cdot n^{\frac{27}{3}} = 3n^9 $$

Answer:

• (A) \(3n^3\) units
• (B) \(3n^9\) units (Correct answer)
• (C) \(27n^3\) units
• (D) \(27n^9\) units