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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{3}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{3}{5} . (\frac{-1}{2}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
2. \(\left(a^{\frac{5}{6}}\right)^{1}\\= a^{ \frac{5}{6} . 1 }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
3. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-2}{5}}\\= a^{ \frac{-1}{2} . (\frac{-2}{5}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
4. \(\left(a^{-1}\right)^{\frac{2}{3}}\\= a^{ -1 . \frac{2}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
5. \(\left(x^{\frac{5}{6}}\right)^{\frac{-1}{4}}\\= x^{ \frac{5}{6} . (\frac{-1}{4}) }= x^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ x^{5} }}=\frac{1}{\sqrt[24]{ x^{5} }}. \color{purple}{\frac{\sqrt[24]{ x^{19} }}{\sqrt[24]{ x^{19} }}} \\=\frac{\sqrt[24]{ x^{19} }}{|x|}\\---------------\)
6. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-2}{3} . (\frac{-2}{3}) }= q^{\frac{4}{9}}\\=\sqrt[9]{ q^{4} }\\---------------\)
7. \(\left(a^{\frac{-1}{2}}\right)^{1}\\= a^{ \frac{-1}{2} . 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
8. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-2}{5} . (\frac{-5}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
9. \(\left(a^{\frac{-1}{2}}\right)^{-2}\\= a^{ \frac{-1}{2} . (-2) }= a^{1}\\\\---------------\)
10. \(\left(a^{\frac{5}{6}}\right)^{\frac{2}{5}}\\= a^{ \frac{5}{6} . \frac{2}{5} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
11. \(\left(y^{\frac{-4}{3}}\right)^{\frac{5}{2}}\\= y^{ \frac{-4}{3} . \frac{5}{2} }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
12. \(\left(y^{\frac{-3}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-3}{2} . (\frac{-1}{2}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)