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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-1}{2} . (\frac{-1}{4}) }= q^{\frac{1}{8}}\\=\sqrt[8]{ q }\\---------------\)
2. \(\left(q^{\frac{4}{3}}\right)^{\frac{-2}{3}}\\= q^{ \frac{4}{3} . (\frac{-2}{3}) }= q^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ q^{8} }}=\frac{1}{\sqrt[9]{ q^{8} }}. \color{purple}{\frac{\sqrt[9]{ q }}{\sqrt[9]{ q }}} \\=\frac{\sqrt[9]{ q }}{q}\\---------------\)
3. \(\left(a^{\frac{2}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{2}{3} . (\frac{-4}{3}) }= a^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ a^{8} }}=\frac{1}{\sqrt[9]{ a^{8} }}. \color{purple}{\frac{\sqrt[9]{ a }}{\sqrt[9]{ a }}} \\=\frac{\sqrt[9]{ a }}{a}\\---------------\)
4. \(\left(a^{\frac{2}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{2}{5} . (\frac{-3}{5}) }= a^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ a^{6} }}=\frac{1}{\sqrt[25]{ a^{6} }}. \color{purple}{\frac{\sqrt[25]{ a^{19} }}{\sqrt[25]{ a^{19} }}} \\=\frac{\sqrt[25]{ a^{19} }}{a}\\---------------\)
5. \(\left(x^{2}\right)^{\frac{3}{2}}\\= x^{ 2 . \frac{3}{2} }= x^{3}\\\\---------------\)
6. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{3}}\\= q^{ \frac{1}{2} . (\frac{-5}{3}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
7. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{3} . (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
8. \(\left(x^{\frac{5}{6}}\right)^{\frac{1}{2}}\\= x^{ \frac{5}{6} . \frac{1}{2} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
9. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-4}{5} . (\frac{-1}{2}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
10. \(\left(q^{\frac{-5}{2}}\right)^{-1}\\= q^{ \frac{-5}{2} . (-1) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
11. \(\left(a^{-1}\right)^{\frac{-1}{2}}\\= a^{ -1 . (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\left(q^{\frac{-5}{4}}\right)^{\frac{1}{3}}\\= q^{ \frac{-5}{4} . \frac{1}{3} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)