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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{6}}\right)^{\frac{1}{4}}\\= x^{ \frac{1}{6} . \frac{1}{4} }= x^{\frac{1}{24}}\\=\sqrt[24]{ x }\\---------------\)
2. \(\left(q^{\frac{4}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{4}{3} . \frac{1}{2} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
3. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-3}{4} . (\frac{-1}{3}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
4. \(\left(x^{-1}\right)^{\frac{-1}{5}}\\= x^{ -1 . (\frac{-1}{5}) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
5. \(\left(x^{\frac{4}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{4}{3} . \frac{1}{3} }= x^{\frac{4}{9}}\\=\sqrt[9]{ x^{4} }\\---------------\)
6. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-3}{4} . (\frac{-3}{4}) }= a^{\frac{9}{16}}\\=\sqrt[16]{ a^{9} }\\---------------\)
7. \(\left(x^{\frac{-5}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{-5}{3} . \frac{2}{3} }= x^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ x^{10} }}\\=\frac{1}{x.\sqrt[9]{ x }}=\frac{1}{x.\sqrt[9]{ x }} \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x^{2}}\\---------------\)
8. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{3} . \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
9. \(\left(y^{\frac{3}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{3}{2} . \frac{1}{2} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
10. \(\left(a^{\frac{5}{3}}\right)^{\frac{-1}{4}}\\= a^{ \frac{5}{3} . (\frac{-1}{4}) }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
11. \(\left(q^{\frac{1}{4}}\right)^{-1}\\= q^{ \frac{1}{4} . (-1) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
12. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-1}{3} . (\frac{-4}{5}) }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)