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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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