What exponent would make the two expressions equivalent: (3^3)x=3^24?(1 point)

Responses

27
27

15
15

8
8

21

1 answer

To solve for the exponent \( x \) that makes the two expressions equivalent, we start with the equation:

\[ (3^3)x = 3^{24} \]

We can rewrite the left side by first simplifying \( (3^3)x \) as \( 3^{3x} \):

\[ 3^{3x} = 3^{24} \]

Since both sides have the same base (3), we can set the exponents equal to each other:

\[ 3x = 24 \]

Now, solve for \( x \):

\[ x = \frac{24}{3} \] \[ x = 8 \]

Thus, the exponent that makes the two expressions equivalent is \( 8 \).

The correct response is:

8.