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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{6}}\right)^{\frac{4}{3}}\\= x^{ \frac{5}{6} . \frac{4}{3} }= x^{\frac{10}{9}}\\=\sqrt[9]{ x^{10} }=x.\sqrt[9]{ x }\\---------------\)
2. \(\left(a^{-1}\right)^{\frac{5}{6}}\\= a^{ -1 . \frac{5}{6} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
3. \(\left(x^{1}\right)^{\frac{3}{2}}\\= x^{ 1 . \frac{3}{2} }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
4. \(\left(y^{\frac{5}{3}}\right)^{\frac{1}{6}}\\= y^{ \frac{5}{3} . \frac{1}{6} }= y^{\frac{5}{18}}\\=\sqrt[18]{ y^{5} }\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{2} . \frac{1}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
6. \(\left(y^{\frac{-2}{3}}\right)^{-1}\\= y^{ \frac{-2}{3} . (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
7. \(\left(q^{\frac{2}{5}}\right)^{-1}\\= q^{ \frac{2}{5} . (-1) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
8. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)
9. \(\left(x^{\frac{-3}{2}}\right)^{\frac{4}{3}}\\= x^{ \frac{-3}{2} . \frac{4}{3} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
10. \(\left(a^{-1}\right)^{-1}\\= a^{ -1 . (-1) }= a^{1}\\\\---------------\)
11. \(\left(y^{\frac{-1}{6}}\right)^{\frac{4}{5}}\\= y^{ \frac{-1}{6} . \frac{4}{5} }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
12. \(\left(y^{-2}\right)^{\frac{-1}{6}}\\= y^{ -2 . (\frac{-1}{6}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)