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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{2}\right)^{\frac{1}{2}}\\= a^{ 2 . \frac{1}{2} }= a^{1}\\\\---------------\)
2. \(\left(y^{\frac{-1}{2}}\right)^{-1}\\= y^{ \frac{-1}{2} . (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
3. \(\left(y^{-2}\right)^{\frac{1}{3}}\\= y^{ -2 . \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
4. \(\left(x^{\frac{1}{3}}\right)^{\frac{5}{3}}\\= x^{ \frac{1}{3} . \frac{5}{3} }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)
5. \(\left(y^{\frac{3}{5}}\right)^{\frac{-1}{5}}\\= y^{ \frac{3}{5} . (\frac{-1}{5}) }= y^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ y^{3} }}=\frac{1}{\sqrt[25]{ y^{3} }}. \color{purple}{\frac{\sqrt[25]{ y^{22} }}{\sqrt[25]{ y^{22} }}} \\=\frac{\sqrt[25]{ y^{22} }}{y}\\---------------\)
6. \(\left(y^{\frac{-5}{4}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-5}{4} . (\frac{-2}{3}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
7. \(\left(q^{\frac{3}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{3}{4} . \frac{1}{2} }= q^{\frac{3}{8}}\\=\sqrt[8]{ q^{3} }\\---------------\)
8. \(\left(y^{\frac{1}{3}}\right)^{\frac{1}{5}}\\= y^{ \frac{1}{3} . \frac{1}{5} }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
9. \(\left(a^{1}\right)^{\frac{-1}{4}}\\= a^{ 1 . (\frac{-1}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
10. \(\left(y^{-1}\right)^{\frac{2}{3}}\\= y^{ -1 . \frac{2}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
11. \(\left(q^{-2}\right)^{\frac{1}{5}}\\= q^{ -2 . \frac{1}{5} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
12. \(\left(a^{\frac{1}{2}}\right)^{1}\\= a^{ \frac{1}{2} . 1 }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)