Answer:
[tex]\displaystyle n^3-\frac{1}{n^{2}}[/tex]
Step-by-step explanation:
Exponents Properties
We need to recall the following properties of exponents:
[tex](a^x)^y=(a^y)^x=a^{xy}[/tex]
[tex]\displaystyle a^{-x}=\frac{1}{a^x}[/tex]
We are given the expression:
[tex]2^m=n[/tex]
We need to express the following expression in terms of n.
[tex]8^m-4^{-m}[/tex]
It's necessary to modify the expression to use the given equivalence.
Recall [tex]8=2^3 \text{ and }4 = 2^2[/tex]. Thus:
[tex](2^3)^m-(2^2)^{-m}[/tex]
Applying the property:
[tex](2^m)^3-(2^m)^{-2}[/tex]
Substituting the given expression:
[tex]n^3-n^{-2}[/tex]
Or, equivalently:
[tex]\mathbf{\displaystyle 8^m-4^{-m}= n^3-\frac{1}{n^{2}}}[/tex]
