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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{2}{5}}\right)^{\frac{3}{4}}\\= x^{ \frac{2}{5} . \frac{3}{4} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
2. \(\left(y^{\frac{1}{3}}\right)^{\frac{-5}{6}}\\= y^{ \frac{1}{3} . (\frac{-5}{6}) }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
3. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-4}{5} . (\frac{-2}{3}) }= a^{\frac{8}{15}}\\=\sqrt[15]{ a^{8} }\\---------------\)
4. \(\left(y^{\frac{5}{6}}\right)^{1}\\= y^{ \frac{5}{6} . 1 }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
5. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{2}}\\= q^{ \frac{1}{2} . (\frac{-5}{2}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
6. \(\left(a^{\frac{2}{5}}\right)^{\frac{-2}{5}}\\= a^{ \frac{2}{5} . (\frac{-2}{5}) }= a^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ a^{4} }}=\frac{1}{\sqrt[25]{ a^{4} }}. \color{purple}{\frac{\sqrt[25]{ a^{21} }}{\sqrt[25]{ a^{21} }}} \\=\frac{\sqrt[25]{ a^{21} }}{a}\\---------------\)
7. \(\left(y^{\frac{1}{2}}\right)^{-1}\\= y^{ \frac{1}{2} . (-1) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
8. \(\left(a^{\frac{2}{3}}\right)^{-1}\\= a^{ \frac{2}{3} . (-1) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
9. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-5}{6} . (\frac{-5}{3}) }= q^{\frac{25}{18}}\\=\sqrt[18]{ q^{25} }=|q|.\sqrt[18]{ q^{7} }\\---------------\)
10. \(\left(q^{\frac{5}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{5}{3} . (\frac{-1}{2}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
11. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-2}{5} . (\frac{-1}{6}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
12. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)