Question

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

21
21

8
8

15
15

27

Answer 1

To solve the equation \((3^3)^x = 3^{24}\), we can use the power of a power property, which states that \((a^m)^n = a^{m \cdot n}\).

Applying this to the left side, we have:

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

So the equation becomes:

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

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

\[
3x = 24
\]

Now, divide both sides by 3:

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

Thus, the exponent that makes the two expressions equivalent is:

**8**