If `3^x=900` ,then find `3^(x+2)` and `3^(x-2)`.

Explanation

To solve the problem, we need to find the values of \(3^{(x+2)}\) and \(3^{(x-2)}\) given that \(3^x = 900\).

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ 3^x = 900 \]

2. **Find \(3^{(x+2)}\):**
- We can express \(3^{(x+2)}\) using the property of exponents:
\[ 3^{(x+2)} = 3^x \cdot 3^2 \]
- Substitute \(3^x\) with 900:
\[ 3^{(x+2)} = 900 \cdot 3^2 \]
- Calculate \(3^2\):
\[ 3^2 = 9 \]
- Now substitute back:
\[ 3^{(x+2)} = 900 \cdot 9 \]
- Perform the multiplication:
\[ 3^{(x+2)} = 8100 \]

3. **Find \(3^{(x-2)}\):**
- Similarly, we can express \(3^{(x-2)}\):
\[ 3^{(x-2)} = \frac{3^x}{3^2} \]
- Substitute \(3^x\) with 900:
\[ 3^{(x-2)} = \frac{900}{3^2} \]
- Again, calculate \(3^2\):
\[ 3^{(x-2)} = \frac{900}{9} \]
- Perform the division:
\[ 3^{(x-2)} = 100 \]

### Final Results:
- \(3^{(x+2)} = 8100\)
- \(3^{(x-2)} = 100\)