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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{1}\right)^{\frac{-5}{6}}\\= y^{ 1 . (\frac{-5}{6}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
2. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{3} . \frac{1}{2} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
3. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-1}{2} . (\frac{-1}{4}) }= q^{\frac{1}{8}}\\=\sqrt[8]{ q }\\---------------\)
4. \(\left(a^{\frac{-2}{3}}\right)^{\frac{5}{3}}\\= a^{ \frac{-2}{3} . \frac{5}{3} }= a^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ a^{10} }}\\=\frac{1}{a.\sqrt[9]{ a }}=\frac{1}{a.\sqrt[9]{ a }} \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a^{2}}\\---------------\)
5. \(\left(q^{\frac{2}{3}}\right)^{\frac{3}{2}}\\= q^{ \frac{2}{3} . \frac{3}{2} }= q^{1}\\\\---------------\)
6. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
7. \(\left(q^{\frac{4}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{4}{3} . \frac{1}{5} }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
8. \(\left(q^{\frac{5}{3}}\right)^{\frac{-2}{3}}\\= q^{ \frac{5}{3} . (\frac{-2}{3}) }= q^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ q^{10} }}\\=\frac{1}{q.\sqrt[9]{ q }}=\frac{1}{q.\sqrt[9]{ q }} \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q^{2}}\\---------------\)
9. \(\left(q^{\frac{-5}{6}}\right)^{\frac{5}{4}}\\= q^{ \frac{-5}{6} . \frac{5}{4} }= q^{\frac{-25}{24}}\\=\frac{1}{\sqrt[24]{ q^{25} }}\\=\frac{1}{|q|.\sqrt[24]{ q }}=\frac{1}{|q|.\sqrt[24]{ q }} \color{purple}{\frac{\sqrt[24]{ q^{23} }}{\sqrt[24]{ q^{23} }}} \\=\frac{\sqrt[24]{ q^{23} }}{|q^{2}|}\\---------------\)
10. \(\left(a^{\frac{-5}{3}}\right)^{\frac{1}{6}}\\= a^{ \frac{-5}{3} . \frac{1}{6} }= a^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ a^{5} }}=\frac{1}{\sqrt[18]{ a^{5} }}. \color{purple}{\frac{\sqrt[18]{ a^{13} }}{\sqrt[18]{ a^{13} }}} \\=\frac{\sqrt[18]{ a^{13} }}{|a|}\\---------------\)
11. \(\left(x^{\frac{1}{6}}\right)^{\frac{-4}{3}}\\= x^{ \frac{1}{6} . (\frac{-4}{3}) }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
12. \(\left(q^{\frac{-3}{5}}\right)^{\frac{1}{2}}\\= q^{ \frac{-3}{5} . \frac{1}{2} }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)