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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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