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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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