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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{4}}\right)^{\frac{-2}{3}}\\= q^{ \frac{1}{4} . (\frac{-2}{3}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
2. \(\left(y^{-1}\right)^{\frac{-5}{3}}\\= y^{ -1 . (\frac{-5}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
3. \(\left(y^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{-2}{3} . \frac{1}{2} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
4. \(\left(q^{-1}\right)^{\frac{1}{6}}\\= q^{ -1 . \frac{1}{6} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
5. \(\left(y^{\frac{-1}{3}}\right)^{2}\\= y^{ \frac{-1}{3} . 2 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
6. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(\left(y^{\frac{-1}{5}}\right)^{\frac{2}{5}}\\= y^{ \frac{-1}{5} . \frac{2}{5} }= y^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ y^{2} }}=\frac{1}{\sqrt[25]{ y^{2} }}. \color{purple}{\frac{\sqrt[25]{ y^{23} }}{\sqrt[25]{ y^{23} }}} \\=\frac{\sqrt[25]{ y^{23} }}{y}\\---------------\)
8. \(\left(a^{1}\right)^{1}\\= a^{ 1 . 1 }= a^{1}\\\\---------------\)
9. \(\left(y^{\frac{1}{3}}\right)^{1}\\= y^{ \frac{1}{3} . 1 }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
10. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-3}{5} . (\frac{-3}{2}) }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
11. \(\left(q^{1}\right)^{\frac{1}{3}}\\= q^{ 1 . \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
12. \(\left(y^{1}\right)^{\frac{5}{6}}\\= y^{ 1 . \frac{5}{6} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)