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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-3}{5}}\right)^{\frac{1}{6}}\\= y^{ \frac{-3}{5} . \frac{1}{6} }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
2. \(\left(q^{1}\right)^{\frac{-2}{5}}\\= q^{ 1 . (\frac{-2}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
3. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-2}{5} . (\frac{-2}{3}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
4. \(\left(x^{\frac{-1}{4}}\right)^{\frac{5}{2}}\\= x^{ \frac{-1}{4} . \frac{5}{2} }= x^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ x^{5} }}=\frac{1}{\sqrt[8]{ x^{5} }}. \color{purple}{\frac{\sqrt[8]{ x^{3} }}{\sqrt[8]{ x^{3} }}} \\=\frac{\sqrt[8]{ x^{3} }}{|x|}\\---------------\)
5. \(\left(y^{\frac{-3}{4}}\right)^{\frac{1}{4}}\\= y^{ \frac{-3}{4} . \frac{1}{4} }= y^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ y^{3} }}=\frac{1}{\sqrt[16]{ y^{3} }}. \color{purple}{\frac{\sqrt[16]{ y^{13} }}{\sqrt[16]{ y^{13} }}} \\=\frac{\sqrt[16]{ y^{13} }}{|y|}\\---------------\)
6. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{2}{3} . (\frac{-1}{2}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
7. \(\left(y^{\frac{1}{5}}\right)^{-1}\\= y^{ \frac{1}{5} . (-1) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
8. \(\left(a^{\frac{-3}{5}}\right)^{\frac{5}{2}}\\= a^{ \frac{-3}{5} . \frac{5}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
9. \(\left(a^{1}\right)^{\frac{5}{3}}\\= a^{ 1 . \frac{5}{3} }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
10. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-1}{4} . (\frac{-1}{6}) }= q^{\frac{1}{24}}\\=\sqrt[24]{ q }\\---------------\)
11. \(\left(a^{\frac{1}{5}}\right)^{1}\\= a^{ \frac{1}{5} . 1 }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
12. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-5}{2}}\\= x^{ \frac{-5}{3} . (\frac{-5}{2}) }= x^{\frac{25}{6}}\\=\sqrt[6]{ x^{25} }=|x^{4}|.\sqrt[6]{ x }\\---------------\)