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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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