The value cannot be determined from the information gives
B
`3^(8)`
C
`9^(3)`
D
`27^(4)`
Text Solution
AI Generated Solution
The correct Answer is:
To solve the problem, we need to find the value of \( 9^a \cdot 3^b \) given that \( 2a + b = 8 \).
### Step-by-step Solution:
1. **Rewrite \( 9^a \)**:
We know that \( 9 \) can be expressed as \( 3^2 \). Therefore, we can rewrite \( 9^a \) as:
\[
9^a = (3^2)^a = 3^{2a}
\]
2. **Combine the expressions**:
Now we can express the entire expression \( 9^a \cdot 3^b \) as:
\[
9^a \cdot 3^b = 3^{2a} \cdot 3^b
\]
3. **Use the property of exponents**:
Since the bases are the same, we can add the exponents:
\[
3^{2a} \cdot 3^b = 3^{2a + b}
\]
4. **Substitute the given equation**:
We know from the problem that \( 2a + b = 8 \). Therefore, we can substitute \( 2a + b \) with \( 8 \):
\[
3^{2a + b} = 3^8
\]
5. **Final result**:
Thus, the value of \( 9^a \cdot 3^b \) is:
\[
3^8
\]
### Conclusion:
The final answer is \( 3^8 \).
