Question

write 5^-0.6 as a root

Answer 1

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:

\[
\frac{1}{\sqrt[5]{5^3}}
\]