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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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