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professorlopes001
Hi.... your answer is below:

[tex]\left( 4.x^{a} \right)^{b}=\dfrac{256}{x^{8}}\rightarrow 4^{b}x^{ab}=256x^{-8}\rightarrow 2^{2b}.\,x^{ab}=2^{8}.\,x^{-8}\rightarrow\\ \text{by comparison}\\ 2^{2b}=2^{8}\rightarrow 2b=8\rightarrow \boxed{b=4}\\ x^{ab}=x^{-8}\rightarrow x^{4a}=x^{-8}\rightarrow 4a=-8\rightarrow \boxed{a=-2}[/tex]

Thanks....

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