Answer:
[tex]\large\boxed{8n^{18}}[/tex]
Step-by-step explanation:
The formula of an area of a square:
[tex]A=s^2[/tex]
s - side length
We have
[tex]A=64n^{36}[/tex]
Method 1:
Substitute:
[tex]s^2=64n^{36}[/tex]
[tex]s^2=8^2n^{18\cdot2}[/tex] use [tex](a^n)^m=a^{nm}[/tex]
[tex]s^2=8^2(n^{18})^2[/tex] use [tex](ab)^n=a^nb^n[/tex]
[tex]s^2=(8n^{18})^2\to s=8n^{18}[/tex]
Method 2:
Substitute:
[tex]s^2=64n^{36}\to s=\sqrt{64n^{36}}[/tex] use [tex]\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]
[tex]s=\sqrt{64}\cdot\sqrt{n^{36}}[/tex]
[tex]s=8\sqrt{n^{(18)(2)}[/tex] use [tex](a^n)^m=a^{nm}[/tex]
[tex]s=8\sqrt{(n^{18})^2}[/tex] use [tex]\sqrt{a^2}=a[/tex] for [tex]a\geq0[/tex]
[tex]s=8n^{18}[/tex]