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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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