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

Answer 1

To find the value of X that makes the two expressions equivalent, we need to set the exponents equal to each other.

(3^3)^X = 3^24

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

3^(3*X) = 3^24

Now, since the bases (3) are the same on both sides of the equation, we can set the exponents equal to each other:

3*X = 24

Divide both sides by 3:

X = 24/3

Simplifying:

X = <<24/3=8>>8

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