Answer :
To simplify the expression \( 2^3 \times 2^2 \), we can use the laws of exponents. One of these laws states that when you multiply exponential terms with the same base, you add the exponents. Mathematically, this is written as:
[tex]\[ a^m \times a^n = a^{m+n} \][/tex]
In this problem, the base \( a \) is 2, and the exponents \( m \) and \( n \) are 3 and 2, respectively.
Step 1: Identify the base and the exponents in the given expression:
- Base: 2
- First exponent: 3 (from \( 2^3 \))
- Second exponent: 2 (from \( 2^2 \))
Step 2: Apply the rule \( a^m \times a^n = a^{m+n} \):
[tex]\[ 2^3 \times 2^2 = 2^{3+2} \][/tex]
Step 3: Add the exponents:
[tex]\[ 2^{3+2} = 2^5 \][/tex]
Step 4: Write the simplified expression with the sum of the exponents:
[tex]\[ 2^5 \][/tex]
Thus, the simplified expression is \( 2^5 \). Therefore, the correct answer is:
[tex]\[ \boxed{2^5} \][/tex]
[tex]\[ a^m \times a^n = a^{m+n} \][/tex]
In this problem, the base \( a \) is 2, and the exponents \( m \) and \( n \) are 3 and 2, respectively.
Step 1: Identify the base and the exponents in the given expression:
- Base: 2
- First exponent: 3 (from \( 2^3 \))
- Second exponent: 2 (from \( 2^2 \))
Step 2: Apply the rule \( a^m \times a^n = a^{m+n} \):
[tex]\[ 2^3 \times 2^2 = 2^{3+2} \][/tex]
Step 3: Add the exponents:
[tex]\[ 2^{3+2} = 2^5 \][/tex]
Step 4: Write the simplified expression with the sum of the exponents:
[tex]\[ 2^5 \][/tex]
Thus, the simplified expression is \( 2^5 \). Therefore, the correct answer is:
[tex]\[ \boxed{2^5} \][/tex]
