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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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