Question

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

8
8

27
27

15
15

21

Answer 1

To determine the value of \( x \) that makes the two expressions \( (3^3)x \) and \( 3^{24} \) equivalent, we can set the two expressions equal to each other and solve for \( x \):

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

Using the power of a power property, we can simplify the left-hand side:

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

Since the bases are the same, we can set the exponents equal to each other:

\[
3x = 24
\]

Next, we solve for \( x \):

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

Thus, the exponent that would make the two expressions equivalent is \( \boxed{8} \).