Question

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

options:


15
15

27
27

8
8

21


?

Answer 1

To make the two expressions \((3^3)^x\) and \(3^{24}\) equivalent, we can use the property of exponents that states \((a^m)^n = a^{m \cdot n}\).

So, we start by simplifying the left side:

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

Now, we have the equation:

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

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

\[
3x = 24
\]

Now, solve for \(x\):

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

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

The correct answer is:

**8**