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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{4}}\right)^{1}\\= a^{ \frac{-1}{4} . 1 }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
2. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-1}{4}}\\= a^{ \frac{-1}{5} . (\frac{-1}{4}) }= a^{\frac{1}{20}}\\=\sqrt[20]{ a }\\---------------\)
3. \(\left(y^{\frac{-1}{3}}\right)^{\frac{1}{6}}\\= y^{ \frac{-1}{3} . \frac{1}{6} }= y^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ y }}=\frac{1}{\sqrt[18]{ y }}. \color{purple}{\frac{\sqrt[18]{ y^{17} }}{\sqrt[18]{ y^{17} }}} \\=\frac{\sqrt[18]{ y^{17} }}{|y|}\\---------------\)
4. \(\left(y^{\frac{1}{2}}\right)^{\frac{4}{3}}\\= y^{ \frac{1}{2} . \frac{4}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
5. \(\left(q^{1}\right)^{\frac{-5}{6}}\\= q^{ 1 . (\frac{-5}{6}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
6. \(\left(x^{\frac{3}{2}}\right)^{\frac{5}{4}}\\= x^{ \frac{3}{2} . \frac{5}{4} }= x^{\frac{15}{8}}\\=\sqrt[8]{ x^{15} }=|x|.\sqrt[8]{ x^{7} }\\---------------\)
7. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-1}{5} . (\frac{-5}{6}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
8. \(\left(y^{\frac{-1}{5}}\right)^{-1}\\= y^{ \frac{-1}{5} . (-1) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
9. \(\left(a^{\frac{-3}{4}}\right)^{-1}\\= a^{ \frac{-3}{4} . (-1) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
10. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{2} . (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
11. \(\left(x^{\frac{1}{2}}\right)^{\frac{-4}{5}}\\= x^{ \frac{1}{2} . (\frac{-4}{5}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
12. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-1}{4}}\\= a^{ \frac{-4}{3} . (\frac{-1}{4}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)