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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{6}}\\= y^{ \frac{-1}{2} . (\frac{-1}{6}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
2. \(\left(x^{\frac{5}{3}}\right)^{\frac{-1}{3}}\\= x^{ \frac{5}{3} . (\frac{-1}{3}) }= x^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ x^{5} }}=\frac{1}{\sqrt[9]{ x^{5} }}. \color{purple}{\frac{\sqrt[9]{ x^{4} }}{\sqrt[9]{ x^{4} }}} \\=\frac{\sqrt[9]{ x^{4} }}{x}\\---------------\)
3. \(\left(x^{\frac{5}{4}}\right)^{1}\\= x^{ \frac{5}{4} . 1 }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
4. \(\left(a^{\frac{3}{5}}\right)^{\frac{1}{4}}\\= a^{ \frac{3}{5} . \frac{1}{4} }= a^{\frac{3}{20}}\\=\sqrt[20]{ a^{3} }\\---------------\)
5. \(\left(q^{-1}\right)^{\frac{3}{2}}\\= q^{ -1 . \frac{3}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
6. \(\left(y^{\frac{4}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{4}{3} . (\frac{-1}{2}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
7. \(\left(y^{\frac{-1}{6}}\right)^{1}\\= y^{ \frac{-1}{6} . 1 }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
8. \(\left(q^{-2}\right)^{\frac{2}{3}}\\= q^{ -2 . \frac{2}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
9. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-2}{5}}\\= a^{ \frac{-2}{3} . (\frac{-2}{5}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
10. \(\left(a^{\frac{1}{3}}\right)^{\frac{-5}{2}}\\= a^{ \frac{1}{3} . (\frac{-5}{2}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
11. \(\left(q^{\frac{1}{3}}\right)^{-1}\\= q^{ \frac{1}{3} . (-1) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
12. \(\left(a^{\frac{-1}{6}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{6} . (\frac{-1}{2}) }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)