what exponent would make the two expressions equivalent (3^3)^x=3^24?

Answer 1

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.