Question

What exponent would make the two expressions equivalent: (16 raised to the x power)6=(16 raised to the 18 power?

Answer 1

To find the value of \( x \) that makes the two expressions equivalent, we start with the equation given:

\[
(16^x)^6 = 16^{18}
\]

Using the power of a power property, we can simplify the left side:

\[
16^{6x} = 16^{18}
\]

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

\[
6x = 18
\]

Now, we can solve for \( x \) by dividing both sides by 6:

\[
x = \frac{18}{6} = 3
\]

Therefore, the exponent that makes the two expressions equivalent is

\[
\boxed{3}
\]