Question

Simplify. Express your answer using positive exponents. 2n^8 * 9n^4/9n

Answer 1

To simplify the expression \( \frac{2n^8 \cdot 9n^4}{9n} \), we can start by simplifying it step by step.

1. **Combine the constants and \(n\) terms:**

The constants in the numerator are \(2\) and \(9\):
\[
2 \cdot 9 = 18
\]

For the \(n\) terms in the numerator, we have \(n^8\) and \(n^4\):
\[
n^8 \cdot n^4 = n^{8+4} = n^{12}
\]

Therefore, the numerator becomes:
\[
18n^{12}
\]

2. **Now, divide by \(9n\):**
\[
\frac{18n^{12}}{9n}
\]

The constants \(18\) and \(9\) can be simplified:
\[
\frac{18}{9} = 2
\]

For the \(n\) terms, we apply the quotient rule for exponents:
\[
\frac{n^{12}}{n} = n^{12-1} = n^{11}
\]

3. **Putting it all together:**

Thus, the expression simplifies to:
\[
2n^{11}
\]

The final answer is:
\[
\boxed{2n^{11}}
\]