Question

What exponent would make the two expressions equivalent: (3 to the third power) to the X power = 3 to the twenty fourth power

Answer 1

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

Applying this property, we have:

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

Now our equation becomes:

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

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

\[
3X = 24
\]

To solve for \( X \), divide both sides by 3:

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

Thus, the value of \( X \) that makes the two expressions equivalent is

\[
\boxed{8}
\]