Question

5^(8/5) simplified

Answer 1

To simplify \( 5^{8/5} \), we can rewrite it in terms of a radical.

The expression can be expressed as:

\[
5^{8/5} = \left(5^8\right)^{1/5}
\]

This means we take the fifth root of \( 5^8 \). Simplifying that further:

\[
5^8 = 390625
\]

Thus, we can write:

\[
5^{8/5} = \sqrt[5]{390625}
\]

However, it's simpler to keep it in exponential form.

We can also express the exponent \( 8/5 \) as a combination of an integer and a fractional part:

\[
5^{8/5} = 5^{1.6} = 5^{1 + 0.6} = 5^1 \times 5^{0.6} = 5 \times 5^{0.6}
\]

But unless you need a numeric approximation, \( 5^{8/5} \) is already in a simplified exponential form.

Thus, the final simplified expression remains:

\[
5^{8/5}
\]

Or in decimal form, approximately:

\[
5^{8/5} \approx 11.1803
\]

So the expression \( 5^{8/5} \) in its simplest forms is \( 5^{8/5} \) or approximately \( 11.18 \).