What exponent would make the two expressions equivalent: (3small3)x=3small24

Question

?(1 point)
Responses

15
15

27
27

8
8

21

Answer 1

To find the exponent \( x \) that makes the two expressions equivalent, we need to set up the equation based on the expressions provided:

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

Using the exponentiation rule \( (a^m)^n = a^{m \cdot n} \), we can simplify the left-hand side:

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

Since the bases are the same, we can equate the exponents:

\[ 3x = 24 \]

Now, solve for \( x \):

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

So, the correct exponent \( x \) that makes the two expressions equivalent is:

8