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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{1}\right)^{\frac{-1}{5}}\\= x^{ 1 . (\frac{-1}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
2. \(\left(a^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{2} . \frac{2}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
3. \(\left(a^{\frac{-4}{5}}\right)^{\frac{1}{4}}\\= a^{ \frac{-4}{5} . \frac{1}{4} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
4. \(\left(x^{\frac{1}{2}}\right)^{\frac{4}{5}}\\= x^{ \frac{1}{2} . \frac{4}{5} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
5. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{2} . \frac{1}{2} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
6. \(\left(q^{\frac{3}{4}}\right)^{\frac{5}{2}}\\= q^{ \frac{3}{4} . \frac{5}{2} }= q^{\frac{15}{8}}\\=\sqrt[8]{ q^{15} }=|q|.\sqrt[8]{ q^{7} }\\---------------\)
7. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-1}{4} . (\frac{-1}{3}) }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
8. \(\left(x^{\frac{1}{6}}\right)^{\frac{2}{5}}\\= x^{ \frac{1}{6} . \frac{2}{5} }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
9. \(\left(q^{\frac{3}{5}}\right)^{\frac{3}{5}}\\= q^{ \frac{3}{5} . \frac{3}{5} }= q^{\frac{9}{25}}\\=\sqrt[25]{ q^{9} }\\---------------\)
10. \(\left(a^{-1}\right)^{\frac{1}{5}}\\= a^{ -1 . \frac{1}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
11. \(\left(x^{\frac{4}{5}}\right)^{\frac{-2}{5}}\\= x^{ \frac{4}{5} . (\frac{-2}{5}) }= x^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ x^{8} }}=\frac{1}{\sqrt[25]{ x^{8} }}. \color{purple}{\frac{\sqrt[25]{ x^{17} }}{\sqrt[25]{ x^{17} }}} \\=\frac{\sqrt[25]{ x^{17} }}{x}\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{\frac{5}{3}}\\= q^{ \frac{-1}{2} . \frac{5}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)