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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{1}{3} . \frac{1}{3} }= x^{\frac{1}{9}}\\=\sqrt[9]{ x }\\---------------\)
2. \(\left(a^{\frac{-3}{4}}\right)^{\frac{1}{3}}\\= a^{ \frac{-3}{4} . \frac{1}{3} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
3. \(\left(a^{-1}\right)^{\frac{3}{4}}\\= a^{ -1 . \frac{3}{4} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
4. \(\left(x^{\frac{-4}{5}}\right)^{\frac{2}{5}}\\= x^{ \frac{-4}{5} . \frac{2}{5} }= x^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ x^{8} }}=\frac{1}{\sqrt[25]{ x^{8} }}. \color{purple}{\frac{\sqrt[25]{ x^{17} }}{\sqrt[25]{ x^{17} }}} \\=\frac{\sqrt[25]{ x^{17} }}{x}\\---------------\)
5. \(\left(q^{-1}\right)^{\frac{-1}{5}}\\= q^{ -1 . (\frac{-1}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
6. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-5}{2} . (\frac{-2}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
7. \(\left(y^{\frac{3}{5}}\right)^{-1}\\= y^{ \frac{3}{5} . (-1) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
8. \(\left(a^{\frac{-4}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-4}{3} . \frac{1}{3} }= a^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ a^{4} }}=\frac{1}{\sqrt[9]{ a^{4} }}. \color{purple}{\frac{\sqrt[9]{ a^{5} }}{\sqrt[9]{ a^{5} }}} \\=\frac{\sqrt[9]{ a^{5} }}{a}\\---------------\)
9. \(\left(q^{\frac{1}{3}}\right)^{-1}\\= q^{ \frac{1}{3} . (-1) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
10. \(\left(q^{\frac{5}{6}}\right)^{\frac{-2}{3}}\\= q^{ \frac{5}{6} . (\frac{-2}{3}) }= q^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ q^{5} }}=\frac{1}{\sqrt[9]{ q^{5} }}. \color{purple}{\frac{\sqrt[9]{ q^{4} }}{\sqrt[9]{ q^{4} }}} \\=\frac{\sqrt[9]{ q^{4} }}{q}\\---------------\)
11. \(\left(q^{\frac{-1}{6}}\right)^{\frac{4}{3}}\\= q^{ \frac{-1}{6} . \frac{4}{3} }= q^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ q^{2} }}=\frac{1}{\sqrt[9]{ q^{2} }}. \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q}\\---------------\)
12. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{5}}\\= y^{ \frac{1}{2} . \frac{1}{5} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)