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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{5}}\right)^{-1}\\= x^{ \frac{-2}{5} . (-1) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
2. \(\left(q^{\frac{-3}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{-3}{2} . \frac{1}{2} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
3. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-1}{6}}\\= y^{ \frac{-3}{5} . (\frac{-1}{6}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
4. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-5}{3} . (\frac{-2}{3}) }= x^{\frac{10}{9}}\\=\sqrt[9]{ x^{10} }=x.\sqrt[9]{ x }\\---------------\)
5. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-4}{3} . (\frac{-1}{6}) }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)
6. \(\left(x^{\frac{1}{2}}\right)^{\frac{3}{4}}\\= x^{ \frac{1}{2} . \frac{3}{4} }= x^{\frac{3}{8}}\\=\sqrt[8]{ x^{3} }\\---------------\)
7. \(\left(a^{\frac{1}{6}}\right)^{\frac{-1}{3}}\\= a^{ \frac{1}{6} . (\frac{-1}{3}) }= a^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ a }}=\frac{1}{\sqrt[18]{ a }}. \color{purple}{\frac{\sqrt[18]{ a^{17} }}{\sqrt[18]{ a^{17} }}} \\=\frac{\sqrt[18]{ a^{17} }}{|a|}\\---------------\)
8. \(\left(a^{\frac{2}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{2}{3} . \frac{1}{5} }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
9. \(\left(x^{\frac{-1}{4}}\right)^{\frac{5}{4}}\\= x^{ \frac{-1}{4} . \frac{5}{4} }= x^{\frac{-5}{16}}\\=\frac{1}{\sqrt[16]{ x^{5} }}=\frac{1}{\sqrt[16]{ x^{5} }}. \color{purple}{\frac{\sqrt[16]{ x^{11} }}{\sqrt[16]{ x^{11} }}} \\=\frac{\sqrt[16]{ x^{11} }}{|x|}\\---------------\)
10. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{-1}{3} . \frac{1}{4} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
11. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-2}{3} . (\frac{-2}{5}) }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
12. \(\left(q^{\frac{4}{5}}\right)^{\frac{-3}{2}}\\= q^{ \frac{4}{5} . (\frac{-3}{2}) }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)