Question
Use the Product Rule of Exponents to simplify the expression 24⋅22 .(1 point) Remaining Attempts : 3
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GPT-4o mini
The Product Rule of Exponents states that when you multiply two expressions with the same base, you can add their exponents.
Given the expression \( 24 \cdot 22 \):
1. Notice that the bases are the same (both are base 2).
2. You can add the exponents:
\[
24 + 22 = 26
\]
Thus, \( 24 \cdot 22 = 2^{4} \cdot 2^{2} = 2^{4+2} = 2^{6} \).
So, the simplified expression is \( 2^{6} \).
If you also need the numerical value:
\[
2^6 = 64.
\]
Therefore, the simplified expression is \( 2^6 \) or \( 64 \).
Given the expression \( 24 \cdot 22 \):
1. Notice that the bases are the same (both are base 2).
2. You can add the exponents:
\[
24 + 22 = 26
\]
Thus, \( 24 \cdot 22 = 2^{4} \cdot 2^{2} = 2^{4+2} = 2^{6} \).
So, the simplified expression is \( 2^{6} \).
If you also need the numerical value:
\[
2^6 = 64.
\]
Therefore, the simplified expression is \( 2^6 \) or \( 64 \).
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