<s>[INST] Evaluate $(\sqrt{3})^{11}$ (Evaluate Square Root $3$ to the power of $11$) I know the answer is $243 \sqrt 3$ but in my maths book they got $(\sqrt 3) (\sqrt 3) (\sqrt 3) (\sqrt 3) (\sqrt 3) (\sqrt 3) (\sqrt 3) (\sqrt 3) (\sqrt 3) (\sqrt 3) (\sqrt 3) (\sqrt 3)$ but then they only took the first $5$ out of the $11$ $(\sqrt 3)$s and then got $(3) (3) (3) (3) (3) (3) \sqrt 3$ and then got $3^5 \sqrt 3$
Why are they only using to the first $5$ $(\sqrt 3)$s? What happened to the other $6$ and how did the answer $243 \sqrt3$ arise? Thank you
 [/INST] $$ \sqrt{3}^{11} = \sqrt{3} \cdot \sqrt{3}^{10} = \sqrt{3} \cdot \left(\sqrt{3}^2\right)^5 = \sqrt{3} \cdot 3^5 = 243\sqrt{3}. $$
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