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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{4}}\right)^{\frac{5}{4}}\\= q^{ \frac{-1}{4} . \frac{5}{4} }= q^{\frac{-5}{16}}\\=\frac{1}{\sqrt[16]{ q^{5} }}=\frac{1}{\sqrt[16]{ q^{5} }}. \color{purple}{\frac{\sqrt[16]{ q^{11} }}{\sqrt[16]{ q^{11} }}} \\=\frac{\sqrt[16]{ q^{11} }}{|q|}\\---------------\)
2. \(\left(y^{\frac{2}{3}}\right)^{1}\\= y^{ \frac{2}{3} . 1 }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
3. \(\left(a^{-2}\right)^{\frac{-1}{2}}\\= a^{ -2 . (\frac{-1}{2}) }= a^{1}\\\\---------------\)
4. \(\left(x^{\frac{1}{3}}\right)^{\frac{-2}{5}}\\= x^{ \frac{1}{3} . (\frac{-2}{5}) }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
5. \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{6}}\\= a^{ \frac{1}{6} . \frac{1}{6} }= a^{\frac{1}{36}}\\=\sqrt[36]{ a }\\---------------\)
6. \(\left(x^{1}\right)^{1}\\= x^{ 1 . 1 }= x^{1}\\\\---------------\)
7. \(\left(y^{\frac{2}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{2}{3} . (\frac{-2}{3}) }= y^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ y^{4} }}=\frac{1}{\sqrt[9]{ y^{4} }}. \color{purple}{\frac{\sqrt[9]{ y^{5} }}{\sqrt[9]{ y^{5} }}} \\=\frac{\sqrt[9]{ y^{5} }}{y}\\---------------\)
8. \(\left(y^{\frac{-1}{2}}\right)^{1}\\= y^{ \frac{-1}{2} . 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
9. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-2}{3} . (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
10. \(\left(y^{\frac{4}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{4}{3} . (\frac{-1}{3}) }= y^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ y^{4} }}=\frac{1}{\sqrt[9]{ y^{4} }}. \color{purple}{\frac{\sqrt[9]{ y^{5} }}{\sqrt[9]{ y^{5} }}} \\=\frac{\sqrt[9]{ y^{5} }}{y}\\---------------\)
11. \(\left(q^{\frac{-1}{4}}\right)^{2}\\= q^{ \frac{-1}{4} . 2 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
12. \(\left(q^{\frac{-3}{4}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-3}{4} . (\frac{-1}{5}) }= q^{\frac{3}{20}}\\=\sqrt[20]{ q^{3} }\\---------------\)