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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{2}}\right)^{\frac{5}{3}}\\= a^{ \frac{-1}{2} . \frac{5}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
2. \(\left(a^{\frac{1}{5}}\right)^{\frac{-1}{4}}\\= a^{ \frac{1}{5} . (\frac{-1}{4}) }= a^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ a }}=\frac{1}{\sqrt[20]{ a }}. \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a|}\\---------------\)
3. \(\left(q^{\frac{-1}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{4} . \frac{1}{2} }= q^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ q }}=\frac{1}{\sqrt[8]{ q }}. \color{purple}{\frac{\sqrt[8]{ q^{7} }}{\sqrt[8]{ q^{7} }}} \\=\frac{\sqrt[8]{ q^{7} }}{|q|}\\---------------\)
4. \(\left(q^{\frac{-5}{4}}\right)^{\frac{2}{5}}\\= q^{ \frac{-5}{4} . \frac{2}{5} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
5. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{5}}\\= q^{ \frac{1}{2} . \frac{1}{5} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
6. \(\left(x^{\frac{-2}{3}}\right)^{1}\\= x^{ \frac{-2}{3} . 1 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
7. \(\left(q^{\frac{3}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{3}{5} . (\frac{-1}{5}) }= q^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ q^{3} }}=\frac{1}{\sqrt[25]{ q^{3} }}. \color{purple}{\frac{\sqrt[25]{ q^{22} }}{\sqrt[25]{ q^{22} }}} \\=\frac{\sqrt[25]{ q^{22} }}{q}\\---------------\)
8. \(\left(x^{-1}\right)^{1}\\= x^{ -1 . 1 }= x^{-1}\\=\frac{1}{x}\\---------------\)
9. \(\left(q^{\frac{-1}{2}}\right)^{\frac{5}{4}}\\= q^{ \frac{-1}{2} . \frac{5}{4} }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
10. \(\left(x^{\frac{1}{2}}\right)^{\frac{1}{4}}\\= x^{ \frac{1}{2} . \frac{1}{4} }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
11. \(\left(a^{1}\right)^{\frac{-2}{5}}\\= a^{ 1 . (\frac{-2}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
12. \(\left(a^{\frac{-1}{5}}\right)^{-2}\\= a^{ \frac{-1}{5} . (-2) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)