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To find the exponent that would make the two expressions equivalent, we can equate the exponents of the base 3.
From the given expression, we have (3^3)^x = 3^24.
Using the power of a power rule, we can simplify the left side of the equation:
(3^3)^x = 3^(3x).
Now our equation becomes 3^(3x) = 3^24.
Since the bases on both sides of the equation are the same (3), we can equate the exponents:
3x = 24.
To solve for x, we divide both sides of the equation by 3:
x = 24/3 = 8.
Therefore, an exponent of 8 would make the two expressions equivalent: (3^3)^8 = 3^24.