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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{3}}\right)^{\frac{1}{4}}\\= x^{ \frac{-5}{3} . \frac{1}{4} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
2. \(\left(x^{\frac{5}{3}}\right)^{\frac{-1}{3}}\\= x^{ \frac{5}{3} . (\frac{-1}{3}) }= x^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ x^{5} }}=\frac{1}{\sqrt[9]{ x^{5} }}. \color{purple}{\frac{\sqrt[9]{ x^{4} }}{\sqrt[9]{ x^{4} }}} \\=\frac{\sqrt[9]{ x^{4} }}{x}\\---------------\)
3. \(\left(x^{-1}\right)^{\frac{-3}{2}}\\= x^{ -1 . (\frac{-3}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
4. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-2}{3} . (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
5. \(\left(a^{1}\right)^{\frac{5}{2}}\\= a^{ 1 . \frac{5}{2} }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
6. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-4}{5} . (\frac{-4}{5}) }= y^{\frac{16}{25}}\\=\sqrt[25]{ y^{16} }\\---------------\)
7. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-1}{2} . (\frac{-5}{6}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
8. \(\left(a^{\frac{-1}{3}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{3} . \frac{3}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
9. \(\left(a^{\frac{5}{4}}\right)^{1}\\= a^{ \frac{5}{4} . 1 }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
10. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{2} . \frac{1}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
11. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-1}{3} . (\frac{-2}{3}) }= x^{\frac{2}{9}}\\=\sqrt[9]{ x^{2} }\\---------------\)
12. \(\left(q^{\frac{1}{6}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{6} . (\frac{-1}{2}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)