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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-2}{5}}\right)^{\frac{5}{3}}\\= y^{ \frac{-2}{5} . \frac{5}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
2. \(\left(y^{\frac{5}{6}}\right)^{\frac{-5}{4}}\\= y^{ \frac{5}{6} . (\frac{-5}{4}) }= y^{\frac{-25}{24}}\\=\frac{1}{\sqrt[24]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[24]{ y }}=\frac{1}{|y|.\sqrt[24]{ y }} \color{purple}{\frac{\sqrt[24]{ y^{23} }}{\sqrt[24]{ y^{23} }}} \\=\frac{\sqrt[24]{ y^{23} }}{|y^{2}|}\\---------------\)
3. \(\left(y^{\frac{-3}{2}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-3}{2} . (\frac{-3}{5}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
4. \(\left(a^{2}\right)^{\frac{-1}{4}}\\= a^{ 2 . (\frac{-1}{4}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
5. \(\left(a^{\frac{1}{5}}\right)^{1}\\= a^{ \frac{1}{5} . 1 }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
6. \(\left(a^{1}\right)^{\frac{-5}{4}}\\= a^{ 1 . (\frac{-5}{4}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
7. \(\left(a^{\frac{2}{3}}\right)^{1}\\= a^{ \frac{2}{3} . 1 }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
8. \(\left(y^{\frac{2}{5}}\right)^{\frac{1}{4}}\\= y^{ \frac{2}{5} . \frac{1}{4} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
9. \(\left(q^{\frac{-1}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{5} . \frac{1}{3} }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
10. \(\left(q^{\frac{3}{2}}\right)^{\frac{5}{6}}\\= q^{ \frac{3}{2} . \frac{5}{6} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
11. \(\left(q^{2}\right)^{2}\\= q^{ 2 . 2 }= q^{4}\\\\---------------\)
12. \(\left(q^{\frac{1}{3}}\right)^{\frac{-4}{5}}\\= q^{ \frac{1}{3} . (\frac{-4}{5}) }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)