Vi skriver om alle leddene som toerpotenser.

Steg 1 – Bruk at $5^0 = 1$:

$$\textcolor{steelblue}{5^0} \cdot 2^3 \cdot 8^{-2} \cdot \left(4^{-1}\right)^{-3} = \textcolor{steelblue}{1} \cdot 2^3 \cdot 8^{-2} \cdot \left(4^{-1}\right)^{-3}$$

Steg 2 – Skriv $8$ og $4$ som toerpotenser:

$$8 = 2^3 \qquad \text{og} \qquad 4 = 2^2$$

Steg 3 – Bruk potensregelen $(a^m)^n = a^{m \cdot n}$:

$$\textcolor{tomato}{8^{-2}} = \left(2^3\right)^{-2} = 2^{3 \cdot (-2)} = \textcolor{tomato}{2^{-6}}$$ $$\textcolor{seagreen}{\left(4^{-1}\right)^{-3}} = \left(2^2\right)^{(-1) \cdot (-3)} = 2^{2 \cdot 3} = \textcolor{seagreen}{2^6}$$

Steg 4 – Sett sammen og bruk $a^m \cdot a^n = a^{m+n}$:

$$1 \cdot 2^3 \cdot \textcolor{tomato}{2^{-6}} \cdot \textcolor{seagreen}{2^6} = 2^{3 + (-6) + 6} = 2^3 = \mathbf{\underline{\underline{8}}}$$