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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{6}}\right)^{\frac{3}{4}}\\= a^{ \frac{1}{6} . \frac{3}{4} }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)
2. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{2} . (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
3. \(\left(q^{\frac{-5}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{-5}{4} . \frac{1}{2} }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
4. \(\left(x^{\frac{-4}{5}}\right)^{\frac{4}{3}}\\= x^{ \frac{-4}{5} . \frac{4}{3} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
5. \(\left(a^{\frac{-1}{4}}\right)^{\frac{4}{5}}\\= a^{ \frac{-1}{4} . \frac{4}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
6. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-2}{3} . (\frac{-4}{3}) }= a^{\frac{8}{9}}\\=\sqrt[9]{ a^{8} }\\---------------\)
7. \(\left(x^{\frac{3}{2}}\right)^{\frac{-1}{3}}\\= x^{ \frac{3}{2} . (\frac{-1}{3}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\left(y^{\frac{2}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{2}{3} . \frac{2}{3} }= y^{\frac{4}{9}}\\=\sqrt[9]{ y^{4} }\\---------------\)
9. \(\left(q^{\frac{1}{5}}\right)^{\frac{-4}{5}}\\= q^{ \frac{1}{5} . (\frac{-4}{5}) }= q^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ q^{4} }}=\frac{1}{\sqrt[25]{ q^{4} }}. \color{purple}{\frac{\sqrt[25]{ q^{21} }}{\sqrt[25]{ q^{21} }}} \\=\frac{\sqrt[25]{ q^{21} }}{q}\\---------------\)
10. \(\left(y^{\frac{4}{5}}\right)^{\frac{-3}{2}}\\= y^{ \frac{4}{5} . (\frac{-3}{2}) }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
11. \(\left(y^{\frac{5}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{5}{2} . \frac{1}{2} }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
12. \(\left(a^{-1}\right)^{2}\\= a^{ -1 . 2 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)