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[tex]\begin{array}{c|l}\sf169&\sf13\\\sf13&\sf13\\\sf1\end{array}\\\sf 169=13^2\\\boxed{\begin{array}{l}\sf\sqrt{169}=\sqrt{13^{\diagdown\!\!\!\!2}}=13\end{array}}\\\begin{array}{c|l}\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf 27=3^3\\\sf\sqrt[\sf3]{-27}=\sqrt[\sf\diagdown\!\!\!\!3]{-3^{\diagdown\!\!\!\!3}}=-3\\\begin{array}{c|l}\sf256&\sf2\\\sf128&\sf2\\\sf64&\sf2\\\sf32&\sf2\\\sf16&\sf2\\\sf8&\sf2\\\sf4&\sf2\\\sf2&\sf2\\\sf1\end{array}\\\sf 256=2^8=(2^2)^4[/tex]
[tex]\sf\sqrt[\sf4]{\dfrac{1}{256}}=\dfrac{\sqrt[\sf4]{1}}{\sqrt[\sf\diagdown\!\!\!\!4]{(2^2)^{\diagdown\!\!\!\!\!4}}}=\dfrac{1}{4}\blue{\checkmark}[/tex]
