Answer:
[tex]\frac{1}{w^{36}}[/tex]
Step-by-step explanation:
Given:
[tex](\frac{w^8}{w^2})^{-6}[/tex]
We need to Simplify the equation;
To Simplify the equation we will use Law of indices.
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]\frac{w^8}{w^2} = w^{8-2}= w^6[/tex]
Now we get;
[tex](w^6)^{-6}[/tex]
Now Simplifying equation we will use Law of indices we get;
[tex](x^a)^b=x^{a\times b}[/tex]
[tex](w^6)^{-6} =w^{6\times -6} = w^{-36}[/tex]
Also again Law of Indices states;
[tex]x^{-a}= \frac{1}{x^a}[/tex]
[tex]w^{-36}= \frac{1}{w^{36}}[/tex]
Hence the Final Answer is [tex]\frac{1}{w^{36}}[/tex]
