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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{\frac{-3}{5}}\\= q^{ -1 . (\frac{-3}{5}) }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
2. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\left(a^{\frac{1}{2}}\right)^{\frac{4}{3}}\\= a^{ \frac{1}{2} . \frac{4}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
4. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{5}}\\= y^{ \frac{2}{3} . (\frac{-1}{5}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
5. \(\left(x^{\frac{-1}{2}}\right)^{-1}\\= x^{ \frac{-1}{2} . (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
6. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-2}{3} . (\frac{-5}{6}) }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)
7. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-1}{4}}\\= a^{ \frac{-3}{4} . (\frac{-1}{4}) }= a^{\frac{3}{16}}\\=\sqrt[16]{ a^{3} }\\---------------\)
8. \(\left(y^{\frac{5}{4}}\right)^{1}\\= y^{ \frac{5}{4} . 1 }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
9. \(\left(x^{\frac{4}{3}}\right)^{\frac{-1}{4}}\\= x^{ \frac{4}{3} . (\frac{-1}{4}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
10. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-5}{3}}\\= x^{ \frac{-1}{2} . (\frac{-5}{3}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
11. \(\left(x^{\frac{4}{5}}\right)^{\frac{-1}{3}}\\= x^{ \frac{4}{5} . (\frac{-1}{3}) }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
12. \(\left(y^{\frac{-1}{3}}\right)^{-1}\\= y^{ \frac{-1}{3} . (-1) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)