Question

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

Answer 1

To make the two expressions equivalent, we need to find the same exponent that can be applied to both expressions.

Using the power of a power property, (a^b)^c = a^(b*c), we can simplify the left side of the equation:

(3^3)^z = 3^(3*z)

So the equation becomes:

3^(3*z) = 3^24

Now, we can set the exponents equal to each other:

3*z = 24

Dividing both sides of the equation by 3:

z = 24/3

Simplifying the expression:

z = 8

Therefore, the exponent that would make the two expressions equivalent is z = 8.