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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-3}{5}}\right)^{\frac{3}{5}}\\= q^{ \frac{-3}{5} . \frac{3}{5} }= q^{\frac{-9}{25}}\\=\frac{1}{\sqrt[25]{ q^{9} }}=\frac{1}{\sqrt[25]{ q^{9} }}. \color{purple}{\frac{\sqrt[25]{ q^{16} }}{\sqrt[25]{ q^{16} }}} \\=\frac{\sqrt[25]{ q^{16} }}{q}\\---------------\)
2. \(\left(y^{1}\right)^{\frac{-5}{2}}\\= y^{ 1 . (\frac{-5}{2}) }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
3. \(\left(y^{\frac{-1}{6}}\right)^{\frac{1}{3}}\\= y^{ \frac{-1}{6} . \frac{1}{3} }= y^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ y }}=\frac{1}{\sqrt[18]{ y }}. \color{purple}{\frac{\sqrt[18]{ y^{17} }}{\sqrt[18]{ y^{17} }}} \\=\frac{\sqrt[18]{ y^{17} }}{|y|}\\---------------\)
4. \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{3} . (\frac{-1}{2}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
5. \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{4}}\\= y^{ \frac{1}{3} . (\frac{-1}{4}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
6. \(\left(x^{\frac{1}{4}}\right)^{\frac{5}{4}}\\= x^{ \frac{1}{4} . \frac{5}{4} }= x^{\frac{5}{16}}\\=\sqrt[16]{ x^{5} }\\---------------\)
7. \(\left(q^{\frac{-3}{2}}\right)^{\frac{-3}{5}}\\= q^{ \frac{-3}{2} . (\frac{-3}{5}) }= q^{\frac{9}{10}}\\=\sqrt[10]{ q^{9} }\\---------------\)
8. \(\left(a^{\frac{-3}{4}}\right)^{-2}\\= a^{ \frac{-3}{4} . (-2) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
9. \(\left(q^{\frac{1}{2}}\right)^{\frac{4}{5}}\\= q^{ \frac{1}{2} . \frac{4}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
10. \(\left(y^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= y^{ \frac{-5}{6} . \frac{1}{2} }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
11. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-1}{2} . (\frac{-1}{6}) }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
12. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-1}{6} . (\frac{-3}{5}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)