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Simplify the following expression.
[tex]\[ 2^2 \cdot 2^3 \][/tex]

A. [tex]\( 2^5 \)[/tex]
B. [tex]\( 2(5) \)[/tex]
C. [tex]\( 2^6 \)[/tex]
D. [tex]\( 2(6) \)[/tex]

Sagot :

GinnyAnsweridn
To simplify the expression [tex]\(2^2 \cdot 2^3\)[/tex], follow these steps:

1. Identify the Base and Exponents: The base for both terms is 2. The exponents are 2 and 3.

2. Apply the Laws of Exponents: According to the law [tex]\(a^m \cdot a^n = a^{m+n}\)[/tex], when you multiply two numbers with the same base, you add their exponents.

3. Add the Exponents: Adding the exponents 2 and 3, we get [tex]\(2 + 3 = 5\)[/tex].

4. Combine the Base and New Exponent: This gives us the simplified expression [tex]\(2^5\)[/tex].

So the correct answer is:
A. [tex]\(2^5\)[/tex]
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