Simplifying formulas » Negative and fractional powers

In the following examples the answer has to be written as a power of a.

1a⁵ = a^–5
fifth root(a) = a^¹⁵

ninth root(a^2) = (a²)^¹⁹ = a^²⁹
1a cubic root(a) = 1a¹ · a^¹³ = 1a^⁴³ = a^{^–43}

In the following example the answer has to be written without negative and fractional powers.
a^{^–34} · b^–3 = 1a^³⁴ · 1b³ = 1 fourth root(a^3) · 1b³