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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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