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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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