To write \( 5^{-0.6} \) as a root, we can start by expressing the negative exponent as a reciprocal:
\[ 5^{-0.6} = \frac{1}{5^{0.6}} \]
Next, we can express \( 5^{0.6} \) in terms of a root. The exponent \( 0.6 \) can be rewritten as a fraction:
\[ 0.6 = \frac{6}{10} = \frac{3}{5} \]
Thus, we can express \( 5^{0.6} \) as:
\[ 5^{0.6} = 5^{\frac{3}{5}} = \sqrt[5]{5^3} \]
Now substituting this back, we have:
\[ 5^{-0.6} = \frac{1}{5^{0.6}} = \frac{1}{\sqrt[5]{5^3}} \]
So, \( 5^{-0.6} \) as a root is:
\[ \frac{1}{\sqrt[5]{5^3}} \]
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