For a positive number n where n^6 = 3 what is the value of n^18

Given the equation \(n^6 = 3\), we need to find the value of \(n^{18}\).

### Step 1: Express \(n^{18}\) in terms of \(n^6\)
Notice that \(n^{18}\) can be written as:

\[
n^{18} = (n^6)^3
\]

### Step 2: Substitute \(n^6 = 3\) into the equation
We substitute the value of \(n^6\) into the expression:

\[
n^{18} = (3)^3
\]

### Step 3: Calculate \(3^3\)
\[
n^{18} = 27
\]

### Final Answer:
The value of \(n^{18}\) is \(27\).

Do you have any questions or would you like more details on this problem?

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**Related Questions:**
1. How would the solution change if \(n^6 = 2\) instead of \(3\)?
2. What is the value of \(n^{12}\) given that \(n^6 = 3\)?
3. How can you express \(n^{24}\) in terms of \(n^6\)?
4. What is the general approach to solving for \(n^{m}\) given \(n^k = a\)?
5. How can you solve for \(n\) if \(n^6 = 3\) and you need to express \(n\) explicitly?

**Tip:** When dealing with exponential equations, remember that powers of a number can often be simplified by expressing the required power in terms of a given one.

Learn how to calculate n^18 when n^6 equals 3 with a detailed step-by-step solution. This problem involves exponentiation and equations, specifically solving for higher powers using given values. Suitable for high school students.

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