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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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