1. $$ S(w)=\sqrt{\left(4 w^{2}+1\right)^{3}} $$

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$$ S(w) = (4w^2 + 1)^{3/2} $$ To simplify the expression $$ S(w) = \sqrt{(4w^2 + 1)^3} $$, we can use the property of square roots that states $$ \sqrt{a^2} = |a| $$. First, we can rewrite the expression: $$ S(w) = \sqrt{(4w^2 + 1)^3} = (4w^2 + 1)^{3/2} $$ This means that $$ S(w) $$ is equal to $$ (4w^2 + 1)^{3/2} $$. If we want to express it in a more simplified form, we can leave it as is, or if we need to evaluate it for specific values of $$ w $$, we can substitute those values in. If you have any specific operations or evaluations in mind for $$ S(w) $$, please let me know!

1. \( S(w)=\sqrt{\left(4 w^{2}+1\right)^{3}} \)

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1. \( S(w)=\sqrt{\left(4 w^{2}+1\right)^{3}} \)

UpStudy ThothAI Solution

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