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

1. 8
2. 15
3. 21
4. 27

1 answer

To find the exponent that would make the two expressions equivalent, we can use the property of exponents which states that (a^b)^c = a^(b*c).

In this case, we have (3^3)^x = 3^24.

Using the property of exponents, we can rewrite the left side of the equation as 3^(3*x). Thus, we have 3^(3*x) = 3^24.

Now, since the bases are the same (3), we can set the exponents equal to each other. Therefore, we have 3*x = 24.

To solve for x, we divide both sides of the equation by 3: x = 24/3 = 8.

Therefore, the answer is 8.