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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{6}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{6} . \frac{1}{2} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
2. \(\left(a^{\frac{3}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{3}{2} . (\frac{-1}{2}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
3. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-1}{3} . (\frac{-5}{4}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
4. \(\left(q^{\frac{-3}{2}}\right)^{\frac{-5}{6}}\\= q^{ \frac{-3}{2} . (\frac{-5}{6}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
5. \(\left(x^{1}\right)^{-2}\\= x^{ 1 . (-2) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
6. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)
7. \(\left(y^{\frac{-1}{5}}\right)^{\frac{1}{5}}\\= y^{ \frac{-1}{5} . \frac{1}{5} }= y^{\frac{-1}{25}}\\=\frac{1}{\sqrt[25]{ y }}=\frac{1}{\sqrt[25]{ y }}. \color{purple}{\frac{\sqrt[25]{ y^{24} }}{\sqrt[25]{ y^{24} }}} \\=\frac{\sqrt[25]{ y^{24} }}{y}\\---------------\)
8. \(\left(y^{\frac{2}{5}}\right)^{1}\\= y^{ \frac{2}{5} . 1 }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
9. \(\left(x^{\frac{-5}{2}}\right)^{\frac{-5}{3}}\\= x^{ \frac{-5}{2} . (\frac{-5}{3}) }= x^{\frac{25}{6}}\\=\sqrt[6]{ x^{25} }=|x^{4}|.\sqrt[6]{ x }\\---------------\)
10. \(\left(q^{\frac{5}{4}}\right)^{\frac{-5}{3}}\\= q^{ \frac{5}{4} . (\frac{-5}{3}) }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
11. \(\left(q^{\frac{-4}{5}}\right)^{\frac{1}{4}}\\= q^{ \frac{-4}{5} . \frac{1}{4} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
12. \(\left(y^{\frac{5}{2}}\right)^{\frac{-5}{4}}\\= y^{ \frac{5}{2} . (\frac{-5}{4}) }= y^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ y^{25} }}\\=\frac{1}{|y^{3}|.\sqrt[8]{ y }}=\frac{1}{|y^{3}|.\sqrt[8]{ y }} \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y^{4}|}\\---------------\)