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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{5}}\right)^{\frac{4}{3}}\\= y^{ \frac{-1}{5} . \frac{4}{3} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
2. \(\left(y^{\frac{-3}{4}}\right)^{\frac{1}{2}}\\= y^{ \frac{-3}{4} . \frac{1}{2} }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)
3. \(\left(y^{\frac{1}{6}}\right)^{\frac{3}{4}}\\= y^{ \frac{1}{6} . \frac{3}{4} }= y^{\frac{1}{8}}\\=\sqrt[8]{ y }\\---------------\)
4. \(\left(y^{\frac{3}{4}}\right)^{\frac{-3}{4}}\\= y^{ \frac{3}{4} . (\frac{-3}{4}) }= y^{\frac{-9}{16}}\\=\frac{1}{\sqrt[16]{ y^{9} }}=\frac{1}{\sqrt[16]{ y^{9} }}. \color{purple}{\frac{\sqrt[16]{ y^{7} }}{\sqrt[16]{ y^{7} }}} \\=\frac{\sqrt[16]{ y^{7} }}{|y|}\\---------------\)
5. \(\left(y^{\frac{5}{2}}\right)^{-1}\\= y^{ \frac{5}{2} . (-1) }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
6. \(\left(y^{\frac{1}{5}}\right)^{\frac{-1}{6}}\\= y^{ \frac{1}{5} . (\frac{-1}{6}) }= y^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ y }}=\frac{1}{\sqrt[30]{ y }}. \color{purple}{\frac{\sqrt[30]{ y^{29} }}{\sqrt[30]{ y^{29} }}} \\=\frac{\sqrt[30]{ y^{29} }}{|y|}\\---------------\)
7. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-2}{3} . (\frac{-1}{3}) }= x^{\frac{2}{9}}\\=\sqrt[9]{ x^{2} }\\---------------\)
8. \(\left(x^{\frac{2}{5}}\right)^{\frac{3}{2}}\\= x^{ \frac{2}{5} . \frac{3}{2} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
9. \(\left(a^{-2}\right)^{\frac{-1}{4}}\\= a^{ -2 . (\frac{-1}{4}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
10. \(\left(q^{\frac{1}{5}}\right)^{-1}\\= q^{ \frac{1}{5} . (-1) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
11. \(\left(q^{\frac{-2}{3}}\right)^{\frac{2}{5}}\\= q^{ \frac{-2}{3} . \frac{2}{5} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
12. \(\left(q^{\frac{-5}{3}}\right)^{\frac{5}{4}}\\= q^{ \frac{-5}{3} . \frac{5}{4} }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)