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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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