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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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