Answer :
Of course! Let's break down the solution step-by-step for the given expressions.
### First Expression:
The first expression is \( 2^2 \cdot 2^4 \).
1. Calculate each power separately:
- \( 2^2 = 4 \)
- \( 2^4 = 16 \)
2. Multiply the results together:
[tex]\[ 4 \cdot 16 = 64 \][/tex]
So, the result of \( 2^2 \cdot 2^4 \) is \( 64 \).
### Second Expression:
The second expression involves \( 3^2 \) and the Gamma function, written as \( \gamma \), specifically \( \gamma^3 \).
1. Calculate \( 3^2 \):
[tex]\[ 3^2 = 9 \][/tex]
2. Evaluate the Gamma function at the required value:
- The Gamma function, \(\gamma(n)\), for a positive integer \( n \) is \((n-1)!\).
- For \(\gamma(3)\), we use \(\gamma(3) = 2! = 2\).
3. Combine the results:
[tex]\[ 9 \cdot 2 = 18 \][/tex]
So, the result of \( 3^2 \cdot \gamma(3) \) is \( 18 \).
Therefore, the solutions to the two expressions are:
1. \( 2^2 \cdot 2^4 = 64 \)
2. \( 3^2 \cdot \gamma(3) = 18 \)
Final answers:
[tex]\[ (64, 18.0) \][/tex]
### First Expression:
The first expression is \( 2^2 \cdot 2^4 \).
1. Calculate each power separately:
- \( 2^2 = 4 \)
- \( 2^4 = 16 \)
2. Multiply the results together:
[tex]\[ 4 \cdot 16 = 64 \][/tex]
So, the result of \( 2^2 \cdot 2^4 \) is \( 64 \).
### Second Expression:
The second expression involves \( 3^2 \) and the Gamma function, written as \( \gamma \), specifically \( \gamma^3 \).
1. Calculate \( 3^2 \):
[tex]\[ 3^2 = 9 \][/tex]
2. Evaluate the Gamma function at the required value:
- The Gamma function, \(\gamma(n)\), for a positive integer \( n \) is \((n-1)!\).
- For \(\gamma(3)\), we use \(\gamma(3) = 2! = 2\).
3. Combine the results:
[tex]\[ 9 \cdot 2 = 18 \][/tex]
So, the result of \( 3^2 \cdot \gamma(3) \) is \( 18 \).
Therefore, the solutions to the two expressions are:
1. \( 2^2 \cdot 2^4 = 64 \)
2. \( 3^2 \cdot \gamma(3) = 18 \)
Final answers:
[tex]\[ (64, 18.0) \][/tex]
