What exponent would make the two expressions equivalent: (33)x=324?(1 point)
Responses
A
8
B
27
C
15
D
21
Since 33 is the same as 3^1 * 11^1, we can rewrite the equation as (3^1 * 11^1)^x = 324.
Using the rules of exponents, we can distribute the exponent x to both 3^1 and 11^1:
3^x * 11^x = 324
To determine the value of x, we need to find the prime factorization of 324.
The prime factorization of 324 is 2^2 * 3^4.
To make the two expressions equivalent, the exponents of 3 in both expressions must be equal.
So, the answer is x = 4.
In the given options, the closest value to 4 is option C: 15.
Therefore, the correct answer is C) 15.