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Werk uit m.b.v. de rekenregels

1. \(\left(a^{\frac{-2}{3}}\right)^{\frac{2}{3}}\)
2. \(\left(x^{\frac{3}{5}}\right)^{\frac{-1}{3}}\)
3. \(\left(q^{\frac{3}{2}}\right)^{\frac{3}{4}}\)
4. \(\left(a^{\frac{4}{5}}\right)^{\frac{3}{2}}\)
5. \(\left(a^{-1}\right)^{\frac{-3}{4}}\)
6. \(\left(q^{\frac{4}{3}}\right)^{\frac{2}{5}}\)
7. \(\left(x^{\frac{-2}{5}}\right)^{\frac{-1}{2}}\)
8. \(\left(q^{\frac{-1}{3}}\right)^{-1}\)
9. \(\left(a^{-1}\right)^{-1}\)
10. \(\left(a^{\frac{3}{5}}\right)^{\frac{5}{2}}\)
11. \(\left(x^{\frac{-1}{6}}\right)^{\frac{1}{6}}\)
12. \(\left(x^{\frac{-4}{3}}\right)^{2}\)

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-2}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-2}{3} . \frac{2}{3} }= a^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ a^{4} }}=\frac{1}{\sqrt[9]{ a^{4} }}. \color{purple}{\frac{\sqrt[9]{ a^{5} }}{\sqrt[9]{ a^{5} }}} \\=\frac{\sqrt[9]{ a^{5} }}{a}\\---------------\)
2. \(\left(x^{\frac{3}{5}}\right)^{\frac{-1}{3}}\\= x^{ \frac{3}{5} . (\frac{-1}{3}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
3. \(\left(q^{\frac{3}{2}}\right)^{\frac{3}{4}}\\= q^{ \frac{3}{2} . \frac{3}{4} }= q^{\frac{9}{8}}\\=\sqrt[8]{ q^{9} }=|q|.\sqrt[8]{ q }\\---------------\)
4. \(\left(a^{\frac{4}{5}}\right)^{\frac{3}{2}}\\= a^{ \frac{4}{5} . \frac{3}{2} }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
5. \(\left(a^{-1}\right)^{\frac{-3}{4}}\\= a^{ -1 . (\frac{-3}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
6. \(\left(q^{\frac{4}{3}}\right)^{\frac{2}{5}}\\= q^{ \frac{4}{3} . \frac{2}{5} }= q^{\frac{8}{15}}\\=\sqrt[15]{ q^{8} }\\---------------\)
7. \(\left(x^{\frac{-2}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-2}{5} . (\frac{-1}{2}) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
8. \(\left(q^{\frac{-1}{3}}\right)^{-1}\\= q^{ \frac{-1}{3} . (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
9. \(\left(a^{-1}\right)^{-1}\\= a^{ -1 . (-1) }= a^{1}\\\\---------------\)
10. \(\left(a^{\frac{3}{5}}\right)^{\frac{5}{2}}\\= a^{ \frac{3}{5} . \frac{5}{2} }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
11. \(\left(x^{\frac{-1}{6}}\right)^{\frac{1}{6}}\\= x^{ \frac{-1}{6} . \frac{1}{6} }= x^{\frac{-1}{36}}\\=\frac{1}{\sqrt[36]{ x }}=\frac{1}{\sqrt[36]{ x }}. \color{purple}{\frac{\sqrt[36]{ x^{35} }}{\sqrt[36]{ x^{35} }}} \\=\frac{\sqrt[36]{ x^{35} }}{|x|}\\---------------\)
12. \(\left(x^{\frac{-4}{3}}\right)^{2}\\= x^{ \frac{-4}{3} . 2 }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)