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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{6}}\right)^{\frac{5}{4}}\\= y^{ \frac{-1}{6} . \frac{5}{4} }= y^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ y^{5} }}=\frac{1}{\sqrt[24]{ y^{5} }}. \color{purple}{\frac{\sqrt[24]{ y^{19} }}{\sqrt[24]{ y^{19} }}} \\=\frac{\sqrt[24]{ y^{19} }}{|y|}\\---------------\)
2. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-1}{4} . (\frac{-1}{4}) }= y^{\frac{1}{16}}\\=\sqrt[16]{ y }\\---------------\)
3. \(\left(q^{\frac{5}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{5}{2} . (\frac{-1}{2}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
4. \(\left(y^{1}\right)^{\frac{5}{4}}\\= y^{ 1 . \frac{5}{4} }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
5. \(\left(x^{1}\right)^{\frac{1}{3}}\\= x^{ 1 . \frac{1}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
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. \(\left(q^{1}\right)^{\frac{-5}{3}}\\= q^{ 1 . (\frac{-5}{3}) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
8. \(\left(x^{\frac{5}{4}}\right)^{\frac{1}{5}}\\= x^{ \frac{5}{4} . \frac{1}{5} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
9. \(\left(q^{\frac{1}{4}}\right)^{\frac{-4}{5}}\\= q^{ \frac{1}{4} . (\frac{-4}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
10. \(\left(q^{\frac{2}{3}}\right)^{2}\\= q^{ \frac{2}{3} . 2 }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
11. \(\left(q^{\frac{1}{6}}\right)^{1}\\= q^{ \frac{1}{6} . 1 }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
12. \(\left(q^{\frac{5}{6}}\right)^{\frac{-1}{5}}\\= q^{ \frac{5}{6} . (\frac{-1}{5}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)