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