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

21
8
15
27

1 answer

To determine the exponent that makes the expressions \((3^3)^{\text{?}} = 3^{24}\) equivalent, we can use the property of exponents that states \((a^m)^n = a^{m \cdot n}\).

Let's denote the unknown exponent as \(x\). The left-hand side of the equation can be rewritten as follows:

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

Now we have:

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

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 makes the two expressions equivalent is \(8\).

The answer is 8.