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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{1}\right)^{\frac{1}{5}}\\= x^{ 1 . \frac{1}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
2. \(\left(a^{-1}\right)^{\frac{-1}{4}}\\= a^{ -1 . (\frac{-1}{4}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
3. \(\left(y^{\frac{5}{4}}\right)^{\frac{-1}{4}}\\= y^{ \frac{5}{4} . (\frac{-1}{4}) }= y^{\frac{-5}{16}}\\=\frac{1}{\sqrt[16]{ y^{5} }}=\frac{1}{\sqrt[16]{ y^{5} }}. \color{purple}{\frac{\sqrt[16]{ y^{11} }}{\sqrt[16]{ y^{11} }}} \\=\frac{\sqrt[16]{ y^{11} }}{|y|}\\---------------\)
4. \(\left(y^{\frac{5}{2}}\right)^{\frac{5}{3}}\\= y^{ \frac{5}{2} . \frac{5}{3} }= y^{\frac{25}{6}}\\=\sqrt[6]{ y^{25} }=|y^{4}|.\sqrt[6]{ y }\\---------------\)
5. \(\left(q^{\frac{1}{2}}\right)^{-1}\\= q^{ \frac{1}{2} . (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
6. \(\left(q^{\frac{3}{5}}\right)^{\frac{-2}{5}}\\= q^{ \frac{3}{5} . (\frac{-2}{5}) }= q^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ q^{6} }}=\frac{1}{\sqrt[25]{ q^{6} }}. \color{purple}{\frac{\sqrt[25]{ q^{19} }}{\sqrt[25]{ q^{19} }}} \\=\frac{\sqrt[25]{ q^{19} }}{q}\\---------------\)
7. \(\left(a^{\frac{-2}{5}}\right)^{\frac{3}{2}}\\= a^{ \frac{-2}{5} . \frac{3}{2} }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
8. \(\left(q^{\frac{-2}{5}}\right)^{\frac{4}{5}}\\= q^{ \frac{-2}{5} . \frac{4}{5} }= q^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ q^{8} }}=\frac{1}{\sqrt[25]{ q^{8} }}. \color{purple}{\frac{\sqrt[25]{ q^{17} }}{\sqrt[25]{ q^{17} }}} \\=\frac{\sqrt[25]{ q^{17} }}{q}\\---------------\)
9. \(\left(q^{-1}\right)^{\frac{-4}{5}}\\= q^{ -1 . (\frac{-4}{5}) }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
10. \(\left(q^{1}\right)^{\frac{5}{6}}\\= q^{ 1 . \frac{5}{6} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
11. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-2}{5} . (\frac{-4}{3}) }= a^{\frac{8}{15}}\\=\sqrt[15]{ a^{8} }\\---------------\)
12. \(\left(y^{\frac{2}{5}}\right)^{\frac{-2}{5}}\\= y^{ \frac{2}{5} . (\frac{-2}{5}) }= y^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ y^{4} }}=\frac{1}{\sqrt[25]{ y^{4} }}. \color{purple}{\frac{\sqrt[25]{ y^{21} }}{\sqrt[25]{ y^{21} }}} \\=\frac{\sqrt[25]{ y^{21} }}{y}\\---------------\)