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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{6}}\right)^{-1}\\= q^{ \frac{1}{6} . (-1) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
2. \(\left(a^{\frac{4}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{4}{3} . (\frac{-1}{2}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
3. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-1}{6} . (\frac{-2}{3}) }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)
4. \(\left(x^{-2}\right)^{\frac{5}{4}}\\= x^{ -2 . \frac{5}{4} }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
5. \(\left(y^{\frac{5}{6}}\right)^{\frac{-1}{6}}\\= y^{ \frac{5}{6} . (\frac{-1}{6}) }= y^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ y^{5} }}=\frac{1}{\sqrt[36]{ y^{5} }}. \color{purple}{\frac{\sqrt[36]{ y^{31} }}{\sqrt[36]{ y^{31} }}} \\=\frac{\sqrt[36]{ y^{31} }}{|y|}\\---------------\)
6. \(\left(q^{\frac{1}{2}}\right)^{\frac{-2}{5}}\\= q^{ \frac{1}{2} . (\frac{-2}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
7. \(\left(x^{\frac{-5}{4}}\right)^{\frac{1}{5}}\\= x^{ \frac{-5}{4} . \frac{1}{5} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
8. \(\left(q^{\frac{-3}{4}}\right)^{1}\\= q^{ \frac{-3}{4} . 1 }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
9. \(\left(x^{-1}\right)^{\frac{-1}{2}}\\= x^{ -1 . (\frac{-1}{2}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(\left(x^{1}\right)^{\frac{-1}{4}}\\= x^{ 1 . (\frac{-1}{4}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
11. \(\left(y^{\frac{5}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{5}{3} . \frac{2}{3} }= y^{\frac{10}{9}}\\=\sqrt[9]{ y^{10} }=y.\sqrt[9]{ y }\\---------------\)
12. \(\left(x^{\frac{2}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{2}{5} . \frac{1}{2} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)