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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-2}{3} . (\frac{-1}{2}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
2. \(\left(a^{\frac{1}{5}}\right)^{\frac{5}{6}}\\= a^{ \frac{1}{5} . \frac{5}{6} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
3. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-5}{6} . (\frac{-2}{3}) }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)
4. \(\left(x^{\frac{1}{2}}\right)^{\frac{2}{3}}\\= x^{ \frac{1}{2} . \frac{2}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
5. \(\left(a^{1}\right)^{\frac{-5}{4}}\\= a^{ 1 . (\frac{-5}{4}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
6. \(\left(q^{\frac{2}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{2}{3} . \frac{1}{5} }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
7. \(\left(q^{\frac{5}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{5}{2} . \frac{1}{2} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
8. \(\left(a^{2}\right)^{-1}\\= a^{ 2 . (-1) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
9. \(\left(y^{\frac{1}{2}}\right)^{2}\\= y^{ \frac{1}{2} . 2 }= y^{1}\\\\---------------\)
10. \(\left(x^{\frac{-1}{3}}\right)^{\frac{5}{2}}\\= x^{ \frac{-1}{3} . \frac{5}{2} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
11. \(\left(x^{\frac{3}{5}}\right)^{\frac{-1}{4}}\\= x^{ \frac{3}{5} . (\frac{-1}{4}) }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)
12. \(\left(a^{-2}\right)^{\frac{-5}{6}}\\= a^{ -2 . (\frac{-5}{6}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)