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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-2}{3}}\right)^{-1}\\= q^{ \frac{-2}{3} . (-1) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
2. \(\left(a^{\frac{3}{4}}\right)^{\frac{-1}{3}}\\= a^{ \frac{3}{4} . (\frac{-1}{3}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
3. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-2}{3} . (\frac{-1}{2}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
4. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-1}{5} . (\frac{-4}{3}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
5. \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{4}}\\= y^{ \frac{1}{3} . (\frac{-1}{4}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
6. \(\left(a^{\frac{-5}{6}}\right)^{\frac{2}{3}}\\= a^{ \frac{-5}{6} . \frac{2}{3} }= a^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ a^{5} }}=\frac{1}{\sqrt[9]{ a^{5} }}. \color{purple}{\frac{\sqrt[9]{ a^{4} }}{\sqrt[9]{ a^{4} }}} \\=\frac{\sqrt[9]{ a^{4} }}{a}\\---------------\)
7. \(\left(q^{\frac{-2}{3}}\right)^{\frac{3}{2}}\\= q^{ \frac{-2}{3} . \frac{3}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
8. \(\left(x^{\frac{1}{5}}\right)^{\frac{3}{5}}\\= x^{ \frac{1}{5} . \frac{3}{5} }= x^{\frac{3}{25}}\\=\sqrt[25]{ x^{3} }\\---------------\)
9. \(\left(q^{\frac{1}{5}}\right)^{\frac{4}{3}}\\= q^{ \frac{1}{5} . \frac{4}{3} }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
10. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{2} . \frac{1}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
11. \(\left(x^{\frac{5}{6}}\right)^{\frac{-1}{2}}\\= x^{ \frac{5}{6} . (\frac{-1}{2}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
12. \(\left(y^{\frac{1}{6}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{6} . \frac{1}{2} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)