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

Answer 1

In order to make the two expressions equivalent, we need to set the exponents equal to each other.

So, we have (3^3)^x = 3^24.

Using the property of exponents (a^m)^n = a^(m*n), we can simplify the left side of the equation:

3^(3*x) = 3^24.

Now, since the base is the same on both sides (3), we can set the exponents equal to each other:

3*x = 24.

To solve for x, we divide both sides of the equation by 3:

x = 24/3.

Simplifying, we find that x = 8.

Therefore, an exponent of 8 would make the two expressions equivalent.