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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{5}}\right)^{\frac{-5}{6}}\\= y^{ \frac{1}{5} . (\frac{-5}{6}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
2. \(\left(a^{\frac{1}{6}}\right)^{\frac{-3}{4}}\\= a^{ \frac{1}{6} . (\frac{-3}{4}) }= a^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ a }}=\frac{1}{\sqrt[8]{ a }}. \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a|}\\---------------\)
3. \(\left(q^{\frac{1}{6}}\right)^{1}\\= q^{ \frac{1}{6} . 1 }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
4. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-4}{5} . (\frac{-1}{2}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
5. \(\left(y^{\frac{-1}{3}}\right)^{-1}\\= y^{ \frac{-1}{3} . (-1) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
6. \(\left(y^{\frac{1}{4}}\right)^{-1}\\= y^{ \frac{1}{4} . (-1) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
7. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-2}{3} . (\frac{-3}{2}) }= x^{1}\\\\---------------\)
8. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-5}{2} . (\frac{-2}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
9. \(\left(a^{\frac{-1}{5}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{5} . \frac{3}{4} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
10. \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
11. \(\left(y^{\frac{-5}{4}}\right)^{\frac{1}{6}}\\= y^{ \frac{-5}{4} . \frac{1}{6} }= y^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ y^{5} }}=\frac{1}{\sqrt[24]{ y^{5} }}. \color{purple}{\frac{\sqrt[24]{ y^{19} }}{\sqrt[24]{ y^{19} }}} \\=\frac{\sqrt[24]{ y^{19} }}{|y|}\\---------------\)
12. \(\left(y^{\frac{5}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{5}{4} . (\frac{-1}{2}) }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}. \color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)