To solve the equation
[tex]\[
\frac{7^{16}}{7^{12}} = \frac{7^{-18}}{?}
\][/tex]
we need to simplify and balance the exponents on both sides.
First, simplify the left-hand side:
[tex]\[
\frac{7^{16}}{7^{12}} = 7^{16-12} = 7^4
\][/tex]
So, the equation becomes:
[tex]\[
7^4 = \frac{7^{-18}}{?}
\][/tex]
To balance the equation, the exponents of 7 on both sides must be equal. This means:
[tex]\[
7^4 = 7^{-18} / ?
\][/tex]
Since the bases are the same, we can set the exponents equal to each other to find the missing term:
[tex]\[
4 = -18 / ?
\][/tex]
Solve for the missing term:
[tex]\[
? = -18 / 4 = -4.5
\][/tex]
Therefore, the missing term in the denominator is
[tex]\[
\boxed{-4.5}
\][/tex]
