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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{5}}\right)^{\frac{5}{6}}\\= x^{ \frac{-1}{5} . \frac{5}{6} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
2. \(\left(a^{\frac{3}{4}}\right)^{-1}\\= a^{ \frac{3}{4} . (-1) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
3. \(\left(a^{\frac{4}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{4}{5} . (\frac{-2}{3}) }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
4. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{5}}\\= x^{ \frac{-1}{3} . \frac{1}{5} }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
5. \(\left(q^{\frac{2}{3}}\right)^{1}\\= q^{ \frac{2}{3} . 1 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
6. \(\left(x^{\frac{-1}{4}}\right)^{\frac{5}{4}}\\= x^{ \frac{-1}{4} . \frac{5}{4} }= x^{\frac{-5}{16}}\\=\frac{1}{\sqrt[16]{ x^{5} }}=\frac{1}{\sqrt[16]{ x^{5} }}. \color{purple}{\frac{\sqrt[16]{ x^{11} }}{\sqrt[16]{ x^{11} }}} \\=\frac{\sqrt[16]{ x^{11} }}{|x|}\\---------------\)
7. \(\left(y^{\frac{5}{3}}\right)^{\frac{5}{4}}\\= y^{ \frac{5}{3} . \frac{5}{4} }= y^{\frac{25}{12}}\\=\sqrt[12]{ y^{25} }=|y^{2}|.\sqrt[12]{ y }\\---------------\)
8. \(\left(a^{\frac{-3}{5}}\right)^{1}\\= a^{ \frac{-3}{5} . 1 }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
9. \(\left(q^{\frac{3}{4}}\right)^{\frac{-2}{3}}\\= q^{ \frac{3}{4} . (\frac{-2}{3}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
10. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= x^{ \frac{-1}{2} . \frac{1}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
11. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-2}{3} . (\frac{-2}{5}) }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
12. \(\left(q^{\frac{4}{5}}\right)^{1}\\= q^{ \frac{4}{5} . 1 }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)