\[\boxed{\text{402\ (402).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
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\[степеней:\]
\[\mathbf{a}^{\mathbf{\text{mn}}}\mathbf{=}\left( \mathbf{a}^{\mathbf{m}} \right)^{\mathbf{n}}\mathbf{.}\]
\[\textbf{а)}\ \sqrt{11^{4}} = \sqrt{\left( 11^{2} \right)^{2}} = |11^{2}| =\]
\[= 121\]
\[\textbf{б)}\ \sqrt{4^{6}} = \sqrt{\left( 4^{3} \right)^{2}} = \left| 4^{3} \right| = 64\]
\[\textbf{в)}\ \sqrt{( - 3)^{8}} = \sqrt{\left( \left( - 3^{4} \right) \right)^{2}\ } =\]
\[= \left| ( - 3)^{4} \right| = |81| = 81\]
\[\textbf{г)}\ \sqrt{( - 6)^{4}} = \sqrt{\left( ( - 6)^{2} \right)^{2}\ } =\]
\(= {|( - 6)}^{2}|\ = |36| = 36\)
\[\textbf{д)}\ \sqrt{2^{8} \cdot 3^{2}} = \sqrt{\left( 2^{4} \cdot 3 \right)^{2}} =\]
\[= \left| 2^{4} \cdot 3 \right| = |16| \cdot 3 = 48\]
\[\textbf{е)}\ \sqrt{3^{4} \cdot 5^{6}} = \sqrt{\left( 3^{2} \cdot 5^{3} \right)^{2}} =\]
\[= \left| 3^{2} \cdot 5^{3} \right| = 9 \cdot 125 = 1125\]
\[\textbf{ж)}\ \sqrt{7^{2} \cdot 2^{8}} = \sqrt{\left( 7 \cdot 2^{4} \right)^{2}} =\]
\[= \left| 7 \cdot 2^{4} \right| = 7 \cdot 16 = 112\]
\[\textbf{з)}\ \sqrt{3^{6} \cdot 5^{4}} = \sqrt{\left( 3^{3} \cdot 5^{2} \right)^{2}} =\]
\[= \left| 3^{3} \cdot 5^{2} \right| = 27 \cdot 25 = 135 \cdot 5 =\]
\[= 675\ \]
\[\textbf{и)}\ \sqrt{8^{4} \cdot 5^{6}} = \sqrt{\left( 8^{2} \cdot 5^{3} \right)^{2}} =\]
\[= \left| 8^{2} \cdot 5^{3} \right| = 8 \cdot 25 \cdot 8 \cdot 5 =\]
\[= 200 \cdot 40 = 8000\]