Es gilt \(\sqrt[m]{x^n}=x^{n/m},\; x^m \cdot x^n = x^{m+n},\; \left ( x^m\right)^n = x^{m\cdot n}\).
\(\sqrt[5]{x^{-3/2}}\cdot \sqrt{x^3}\\
=\left ( x^{-3/2}\right)^{1/5} \cdot x^{3/2} \\
= x^{-3/2 \;\cdot\; 1/5} \cdot x^{3/2} \\
=x^{-3/10} \cdot x^{3/2} \\
= x^{-3/10 \; + \; 3/2} \\
=x^{6/5}\\
=\sqrt[5]{x^6}\)
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