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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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