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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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