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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{-1}\right)^{\frac{-5}{2}}\\= a^{ -1 . (\frac{-5}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
2. \(\left(a^{\frac{-1}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{3} . \frac{2}{3} }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)
3. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
4. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{1}{3} . \frac{1}{3} }= a^{\frac{1}{9}}\\=\sqrt[9]{ a }\\---------------\)
5. \(\left(q^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{2} . (\frac{-1}{2}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
6. \(\left(q^{\frac{3}{5}}\right)^{\frac{-3}{5}}\\= q^{ \frac{3}{5} . (\frac{-3}{5}) }= q^{\frac{-9}{25}}\\=\frac{1}{\sqrt[25]{ q^{9} }}=\frac{1}{\sqrt[25]{ q^{9} }}. \color{purple}{\frac{\sqrt[25]{ q^{16} }}{\sqrt[25]{ q^{16} }}} \\=\frac{\sqrt[25]{ q^{16} }}{q}\\---------------\)
7. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-1}{2} . (\frac{-3}{4}) }= y^{\frac{3}{8}}\\=\sqrt[8]{ y^{3} }\\---------------\)
8. \(\left(q^{1}\right)^{\frac{-1}{3}}\\= q^{ 1 . (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
9. \(\left(q^{-1}\right)^{\frac{-2}{3}}\\= q^{ -1 . (\frac{-2}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
10. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-3}{4} . (\frac{-5}{3}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
11. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-4}{3} . (\frac{-4}{3}) }= a^{\frac{16}{9}}\\=\sqrt[9]{ a^{16} }=a.\sqrt[9]{ a^{7} }\\---------------\)
12. \(\left(a^{-1}\right)^{\frac{2}{3}}\\= a^{ -1 . \frac{2}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)