Question

The volume of a cube is 27 n Superscript 27cubic units. What is the length of one side of the cube?
3 n cubed units
3 n Superscript 9 units
27 n cubed units
27 n Superscript 9 units

Answer 1

To find the length of one side of a cube when given its volume, you can use the formula for the volume of a cube, which is:

\[
V = s^3
\]

where \( V \) is the volume and \( s \) is the length of one side. Given that the volume of the cube is \( 27n^{27} \) cubic units, we set up the equation:

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

To solve for \( s \), take the cube root of both sides:

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

The cube root of \( 27 \) is \( 3 \), because \( 3^3 = 27 \). The cube root of \( n^{27} \) is \( n^{9} \), because \( (n^9)^3 = n^{27} \).

Therefore, we have:

\[
s = 3n^9
\]

Thus, the length of one side of the cube is \( 3n^9 \) units.

The correct answer is:

**3 n Superscript 9 units**.