How many zeros are there in the cube of a number that has n zeros?

A number with $n$ zeros can be expressed as $k \times 10^n$, where $k$ is a non-zero digit or a number not ending in zero. For simplicity, we can consider the number $10^n$. This number has $n$ zeros.
For example:

• If $n=1$, the number is $10^1 = 10$ (one zero).
• If $n=2$, the number is $10^2 = 100$ (two zeros).

We need to find the number of zeros in the cube of $10^n$.
The cube of $10^n$ is $(10^n)^3$.

Using the exponent rule $(a^b)^c = a^{b \times c}$:

A number written in the form $10^x$ has $x$ zeros.
Therefore, $10^{3n}$ has $3n$ zeros.

The number of zeros in the cube is $3n$. This matches option (b).

The final answer is $\text{b) } 3n$.