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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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