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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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