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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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