Use two main properties of powers:
1. [tex]\left(\dfrac{1}{a}\right)^n=a^{-n};[/tex]
2. [tex]a^n=a^m\Rightarrow n=m.[/tex]
Consider the equation
[tex]\left(\dfrac{1}{3}\right)^{d-5}=81.[/tex]
Note that:
1. [tex]\left(\dfrac{1}{3}\right)^{d-5}=3^{-1\cdot (d-5)}=3^{-d+5};[/tex]
2. [tex]81=3^4.[/tex]
Then, the equation will take look
[tex]3^{-d+5}=3^4.[/tex]
The bases of the left and right sides are the same, then the powers are the same too.
[tex]-d+5=4.[/tex]
Answer: correct choice is C
