Since the power of 2 is even, the result will be positive.
\[\sqrt{{2}^{2}}+\sqrt[3]{{(-2)}^{3}}+4\sqrt{{(-2)}^{4}}\]
Simplify \(\sqrt{{2}^{2}}\) to \(2\).
\[2+\sqrt[3]{{(-2)}^{3}}+4\sqrt{{(-2)}^{4}}\]
Since the power of 3 is odd, the result will be negative.
\[2+\sqrt[3]{-{2}^{3}}+4\sqrt{{(-2)}^{4}}\]
Simplify \({2}^{3}\) to \(8\).
\[2+\sqrt[3]{-8}+4\sqrt{{(-2)}^{4}}\]
Since the power of 4 is even, the result will be positive.
\[2+\sqrt[3]{-8}+4\sqrt{{2}^{4}}\]
Simplify \(\sqrt{{2}^{4}}\) to \({2}^{2}\).
\[2+\sqrt[3]{-8}+4\times {2}^{2}\]
Simplify exponent.
\[2-2+4\times {2}^{2}\]
Simplify \({2}^{2}\) to \(4\).
\[2-2+4\times 4\]
Simplify \(4\times 4\) to \(16\).
\[2-2+16\]
Simplify \(2-2\) to \(0\).
\[0+16\]
Simplify.
\[16\]
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