To expand \( 3^2 \cdot 4^3 \), we first rewrite the numbers in expanded form.
Starting with \( 3^2 \):
\[ 3^2 = 3 \cdot 3 = 9 \]
Next, for \( 4^3 \):
\[ 4^3 = 4 \cdot 4 \cdot 4 = 16 \cdot 4 = 64 \]
Now, we can multiply the two results together:
\[ 3^2 \cdot 4^3 = 9 \cdot 64 \]
To calculate \( 9 \cdot 64 \):
\[ 9 \cdot 64 = 576 \]
Thus, we have:
\[ 3^2 \cdot 4^3 = 576 \]
Now, we need to check if this is equal to \( 12^5 \). Let's calculate \( 12^5 \):
\[ 12^5 = 12 \cdot 12 \cdot 12 \cdot 12 \cdot 12 \]
Calculating step-by-step:
- \( 12^2 = 144 \)
- \( 12^3 = 12 \cdot 144 = 1728 \)
- \( 12^4 = 12 \cdot 1728 = 20736 \)
- \( 12^5 = 12 \cdot 20736 = 248832 \)
Now we compare:
\[ 3^2 \cdot 4^3 = 576 \] \[ 12^5 = 248832 \]
Clearly, \( 576 \) is not equal to \( 248832 \).
In conclusion:
\[ 3^2 \cdot 4^3 \neq 12^5 \]
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