What exponent would make the two expressions equivalent: (16^x)^6=(16^18)

Answer 1

To find the exponent that would make the two expressions equal, we need to set the exponents equal to each other and solve for x.

(16^x)^6 = (16^18)

To solve this equation, we can use the property of exponents that states: (a^b)^c = a^(b*c)

Therefore, we can rewrite the left side as:

16^(6x) = 16^18

Now, since the base is the same on both sides (16), we can equate the exponents:

6x = 18

To solve for x, divide both sides of the equation by 6:

x = 18/6

Simplifying, we get:

x = 3

So, the exponent that would make the two expressions equivalent is 3.