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

options:

15
15

27
27

8
8

21

?

1 answer

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