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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{-1}{3} . \frac{1}{3} }= x^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ x }}=\frac{1}{\sqrt[9]{ x }}. \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x}\\---------------\)
2. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-5}{3} . (\frac{-4}{5}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
3. \(\left(y^{\frac{2}{3}}\right)^{1}\\= y^{ \frac{2}{3} . 1 }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
4. \(\left(x^{-1}\right)^{\frac{2}{5}}\\= x^{ -1 . \frac{2}{5} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
5. \(\left(x^{\frac{1}{4}}\right)^{\frac{-5}{2}}\\= x^{ \frac{1}{4} . (\frac{-5}{2}) }= x^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ x^{5} }}=\frac{1}{\sqrt[8]{ x^{5} }}. \color{purple}{\frac{\sqrt[8]{ x^{3} }}{\sqrt[8]{ x^{3} }}} \\=\frac{\sqrt[8]{ x^{3} }}{|x|}\\---------------\)
6. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{6}}\\= q^{ \frac{2}{3} . (\frac{-1}{6}) }= q^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ q }}=\frac{1}{\sqrt[9]{ q }}. \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q}\\---------------\)
7. \(\left(y^{1}\right)^{\frac{-3}{5}}\\= y^{ 1 . (\frac{-3}{5}) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
8. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-5}{6}}\\= a^{ \frac{-1}{2} . (\frac{-5}{6}) }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
9. \(\left(q^{\frac{5}{4}}\right)^{\frac{1}{6}}\\= q^{ \frac{5}{4} . \frac{1}{6} }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
10. \(\left(q^{1}\right)^{\frac{-5}{3}}\\= q^{ 1 . (\frac{-5}{3}) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
11. \(\left(x^{\frac{1}{3}}\right)^{1}\\= x^{ \frac{1}{3} . 1 }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
12. \(\left(q^{\frac{1}{6}}\right)^{\frac{2}{3}}\\= q^{ \frac{1}{6} . \frac{2}{3} }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)