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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{1}{3} . \frac{1}{3} }= y^{\frac{1}{9}}\\=\sqrt[9]{ y }\\---------------\)
2. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-3}{5} . (\frac{-3}{2}) }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
3. \(\left(q^{\frac{5}{3}}\right)^{\frac{-2}{5}}\\= q^{ \frac{5}{3} . (\frac{-2}{5}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
4. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-1}{3} . (\frac{-1}{6}) }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
5. \(\left(x^{\frac{2}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{2}{3} . \frac{2}{3} }= x^{\frac{4}{9}}\\=\sqrt[9]{ x^{4} }\\---------------\)
6. \(\left(x^{\frac{5}{4}}\right)^{-1}\\= x^{ \frac{5}{4} . (-1) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
7. \(\left(q^{\frac{1}{3}}\right)^{\frac{3}{2}}\\= q^{ \frac{1}{3} . \frac{3}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
8. \(\left(q^{\frac{4}{3}}\right)^{\frac{3}{5}}\\= q^{ \frac{4}{3} . \frac{3}{5} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
9. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
10. \(\left(x^{\frac{5}{2}}\right)^{\frac{-5}{6}}\\= x^{ \frac{5}{2} . (\frac{-5}{6}) }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
11. \(\left(x^{\frac{-5}{3}}\right)^{\frac{5}{4}}\\= x^{ \frac{-5}{3} . \frac{5}{4} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
12. \(\left(q^{\frac{-2}{3}}\right)^{\frac{5}{3}}\\= q^{ \frac{-2}{3} . \frac{5}{3} }= q^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ q^{10} }}\\=\frac{1}{q.\sqrt[9]{ q }}=\frac{1}{q.\sqrt[9]{ q }} \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q^{2}}\\---------------\)