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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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