Question

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

Answer 1

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

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

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

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

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

\[
6x = 18
\]

Now, solve for \( x \):

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

Therefore, the exponent \( x \) that makes the two expressions equivalent is

\[
\boxed{3}.
\]