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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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