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

Question

Responses

15
15

27
27

21
21

8

Answer 1

To make the two expressions \( (3^3)x \) and \( 3^{24} \) equivalent, we can rewrite the first expression.

Starting with:

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

We can express \( x \) in terms of \( 3^{n} \) as follows:

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

To isolate \( x \), we can divide both sides by \( 3^{3} \):

\[ x = \frac{3^{24}}{3^{3}} = 3^{24 - 3} = 3^{21} \]

Hence, the exponent that would make the two expressions equivalent is:

\[ \boxed{21} \]