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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{2}}\right)^{\frac{1}{4}}\\= q^{ \frac{-5}{2} . \frac{1}{4} }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
2. \(\left(a^{\frac{-1}{6}}\right)^{\frac{1}{6}}\\= a^{ \frac{-1}{6} . \frac{1}{6} }= a^{\frac{-1}{36}}\\=\frac{1}{\sqrt[36]{ a }}=\frac{1}{\sqrt[36]{ a }}. \color{purple}{\frac{\sqrt[36]{ a^{35} }}{\sqrt[36]{ a^{35} }}} \\=\frac{\sqrt[36]{ a^{35} }}{|a|}\\---------------\)
3. \(\left(q^{\frac{-3}{5}}\right)^{1}\\= q^{ \frac{-3}{5} . 1 }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
4. \(\left(a^{\frac{1}{3}}\right)^{2}\\= a^{ \frac{1}{3} . 2 }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
5. \(\left(q^{\frac{2}{3}}\right)^{\frac{1}{3}}\\= q^{ \frac{2}{3} . \frac{1}{3} }= q^{\frac{2}{9}}\\=\sqrt[9]{ q^{2} }\\---------------\)
6. \(\left(y^{\frac{-4}{5}}\right)^{\frac{5}{3}}\\= y^{ \frac{-4}{5} . \frac{5}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
7. \(\left(x^{\frac{-3}{5}}\right)^{\frac{-3}{5}}\\= x^{ \frac{-3}{5} . (\frac{-3}{5}) }= x^{\frac{9}{25}}\\=\sqrt[25]{ x^{9} }\\---------------\)
8. \(\left(y^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{2} . \frac{2}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
9. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-2}{5} . (\frac{-4}{5}) }= y^{\frac{8}{25}}\\=\sqrt[25]{ y^{8} }\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{-4}{3}}\\= q^{ \frac{1}{2} . (\frac{-4}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
11. \(\left(q^{1}\right)^{\frac{1}{3}}\\= q^{ 1 . \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)