What exponent would make the two expressions equivalent: (33)x=324?(1 point)
Responses
21
21
21
8
27
15
The exponent that would make the two expressions equivalent is 3, as 33 raised to the power of 3 is equal to 324. Therefore, the correct response is 3.
To find the exponent that would make the two expressions equivalent, we need to think about exponentiation and how it relates to multiplication. The equation (33)^x = 324 can be rewritten as 3^3x = 3^4.
Since the base (3) is the same on both sides, we can equate the exponents: 3x = 4.
Dividing both sides of the equation by 3, we get x = 4/3.
So, the exponent that would make the two expressions equivalent is x = 4/3.
To find the exponent that would make the two expressions equivalent, we need to solve the equation (33)^x = 324.
First, let's rewrite 324 as a power of 3. 324 can be written as 3^4 since 3^4 = 81 and 81*4 = 324.
Now our equation becomes (33)^x = (3^4)^x.
According to the properties of exponents, we can simplify this to 3^(3x) = 3^4x.
Since the bases (3) are the same, the exponents must also be equal. Therefore, we have 3x = 4x.
To solve for x, we can subtract 4x from both sides of the equation, which gives us -x = 0.
Dividing both sides by -1, we get x = 0.
Therefore, the exponent that makes the two expressions equivalent is x = 0.
Option: 15 is incorrect.
Option: 21 is incorrect.
Option: 27 is incorrect.
Option: 8 is incorrect.
The correct answer is x = 0.