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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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