Bot GPT 4-o mini To determine the value of \( x \) that makes the two expressions \( (3^3)x \) and \( 3^{24} \) equivalent, we can set the two expressions equal to each other and solve for \( x \):
\[ (3^3)^x = 3^{24} \]
Using the power of a power property, we can simplify the left-hand side:
\[ 3^{3x} = 3^{24} \]
Since the bases are the same, we can set the exponents equal to each other:
\[ 3x = 24 \]
Next, we solve for \( x \):
\[ x = \frac{24}{3} = 8 \]
Thus, the exponent that would make the two expressions equivalent is \( \boxed{8} \).
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