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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-2}{3} . (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
2. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{5}}\\= y^{ \frac{-1}{2} . (\frac{-1}{5}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
3. \(\left(y^{\frac{1}{6}}\right)^{\frac{4}{5}}\\= y^{ \frac{1}{6} . \frac{4}{5} }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
4. \(\left(a^{\frac{3}{4}}\right)^{\frac{1}{6}}\\= a^{ \frac{3}{4} . \frac{1}{6} }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)
5. \(\left(q^{\frac{1}{5}}\right)^{\frac{4}{5}}\\= q^{ \frac{1}{5} . \frac{4}{5} }= q^{\frac{4}{25}}\\=\sqrt[25]{ q^{4} }\\---------------\)
6. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-1}{5} . (\frac{-1}{3}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
7. \(\left(y^{\frac{-5}{3}}\right)^{\frac{3}{5}}\\= y^{ \frac{-5}{3} . \frac{3}{5} }= y^{-1}\\=\frac{1}{y}\\---------------\)
8. \(\left(x^{\frac{4}{3}}\right)^{\frac{-1}{4}}\\= x^{ \frac{4}{3} . (\frac{-1}{4}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
9. \(\left(q^{\frac{-4}{5}}\right)^{1}\\= q^{ \frac{-4}{5} . 1 }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
10. \(\left(a^{\frac{-2}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{-2}{5} . \frac{1}{3} }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
11. \(\left(a^{1}\right)^{\frac{-1}{2}}\\= a^{ 1 . (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
12. \(\left(y^{\frac{-3}{2}}\right)^{\frac{-5}{2}}\\= y^{ \frac{-3}{2} . (\frac{-5}{2}) }= y^{\frac{15}{4}}\\=\sqrt[4]{ y^{15} }=|y^{3}|.\sqrt[4]{ y^{3} }\\---------------\)