Question

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

Answer 1

To find the exponent that makes the two expressions equivalent, we start with the given expressions:

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

Using the property of exponents that states \((a^m)^n = a^{m \cdot n}\), we can simplify the left side of the equation:

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

Since the bases on both sides are the same (16), we can set the exponents equal to each other:

\[
6x = 18
\]

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

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

Thus, the exponent that makes the two expressions equivalent is

\[
\boxed{3}.
\]