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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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