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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{5}}\right)^{\frac{-1}{6}}\\= y^{ \frac{1}{5} . (\frac{-1}{6}) }= y^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ y }}=\frac{1}{\sqrt[30]{ y }}. \color{purple}{\frac{\sqrt[30]{ y^{29} }}{\sqrt[30]{ y^{29} }}} \\=\frac{\sqrt[30]{ y^{29} }}{|y|}\\---------------\)
2. \(\left(a^{1}\right)^{\frac{-3}{2}}\\= a^{ 1 . (\frac{-3}{2}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
3. \(\left(x^{1}\right)^{\frac{1}{4}}\\= x^{ 1 . \frac{1}{4} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
4. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-3}{5}}\\= x^{ \frac{-1}{4} . (\frac{-3}{5}) }= x^{\frac{3}{20}}\\=\sqrt[20]{ x^{3} }\\---------------\)
5. \(\left(a^{\frac{-3}{5}}\right)^{\frac{5}{4}}\\= a^{ \frac{-3}{5} . \frac{5}{4} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
6. \(\left(q^{1}\right)^{\frac{-2}{5}}\\= q^{ 1 . (\frac{-2}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
7. \(\left(y^{\frac{1}{3}}\right)^{\frac{3}{4}}\\= y^{ \frac{1}{3} . \frac{3}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
8. \(\left(y^{\frac{5}{6}}\right)^{\frac{4}{5}}\\= y^{ \frac{5}{6} . \frac{4}{5} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
9. \(\left(x^{\frac{-5}{2}}\right)^{-2}\\= x^{ \frac{-5}{2} . (-2) }= x^{5}\\\\---------------\)
10. \(\left(y^{-1}\right)^{\frac{-1}{6}}\\= y^{ -1 . (\frac{-1}{6}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
11. \(\left(a^{-2}\right)^{\frac{-4}{3}}\\= a^{ -2 . (\frac{-4}{3}) }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
12. \(\left(x^{\frac{1}{4}}\right)^{1}\\= x^{ \frac{1}{4} . 1 }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)