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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-5}{3}}\right)^{\frac{4}{3}}\\= a^{ \frac{-5}{3} . \frac{4}{3} }= a^{\frac{-20}{9}}\\=\frac{1}{\sqrt[9]{ a^{20} }}\\=\frac{1}{a^{2}.\sqrt[9]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[9]{ a^{2} }} \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a^{3}}\\---------------\)
2. \(\left(q^{\frac{3}{5}}\right)^{\frac{-4}{5}}\\= q^{ \frac{3}{5} . (\frac{-4}{5}) }= q^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ q^{12} }}=\frac{1}{\sqrt[25]{ q^{12} }}. \color{purple}{\frac{\sqrt[25]{ q^{13} }}{\sqrt[25]{ q^{13} }}} \\=\frac{\sqrt[25]{ q^{13} }}{q}\\---------------\)
3. \(\left(y^{\frac{-4}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-4}{3} . (\frac{-1}{3}) }= y^{\frac{4}{9}}\\=\sqrt[9]{ y^{4} }\\---------------\)
4. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{2} . (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
5. \(\left(q^{\frac{-5}{2}}\right)^{\frac{5}{2}}\\= q^{ \frac{-5}{2} . \frac{5}{2} }= q^{\frac{-25}{4}}\\=\frac{1}{\sqrt[4]{ q^{25} }}\\=\frac{1}{|q^{6}|.\sqrt[4]{ q }}=\frac{1}{|q^{6}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{7}|}\\---------------\)
6. \(\left(q^{\frac{-3}{5}}\right)^{\frac{1}{6}}\\= q^{ \frac{-3}{5} . \frac{1}{6} }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
7. \(\left(a^{\frac{1}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{1}{3} . \frac{2}{3} }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)
8. \(\left(a^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= a^{ \frac{1}{2} . \frac{1}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
9. \(\left(y^{\frac{-2}{3}}\right)^{-1}\\= y^{ \frac{-2}{3} . (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
10. \(\left(a^{\frac{1}{2}}\right)^{\frac{-5}{2}}\\= a^{ \frac{1}{2} . (\frac{-5}{2}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
11. \(\left(a^{-1}\right)^{\frac{-1}{2}}\\= a^{ -1 . (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\left(x^{1}\right)^{\frac{1}{5}}\\= x^{ 1 . \frac{1}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)