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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-1}{4} . (\frac{-3}{2}) }= x^{\frac{3}{8}}\\=\sqrt[8]{ x^{3} }\\---------------\)
2. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
3. \(\left(a^{1}\right)^{\frac{-2}{3}}\\= a^{ 1 . (\frac{-2}{3}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
4. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{2} . (\frac{-1}{2}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
5. \(\left(q^{-1}\right)^{\frac{-1}{3}}\\= q^{ -1 . (\frac{-1}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
6. \(\left(x^{\frac{3}{5}}\right)^{\frac{5}{4}}\\= x^{ \frac{3}{5} . \frac{5}{4} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
7. \(\left(a^{1}\right)^{\frac{-5}{4}}\\= a^{ 1 . (\frac{-5}{4}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
8. \(\left(x^{\frac{-4}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-4}{3} . (\frac{-5}{6}) }= x^{\frac{10}{9}}\\=\sqrt[9]{ x^{10} }=x.\sqrt[9]{ x }\\---------------\)
9. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-2}{3} . (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
10. \(\left(x^{1}\right)^{1}\\= x^{ 1 . 1 }= x^{1}\\\\---------------\)
11. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-5}{6} . (\frac{-5}{6}) }= y^{\frac{25}{36}}\\=\sqrt[36]{ y^{25} }\\---------------\)
12. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-1}{6} . (\frac{-3}{2}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)