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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{-1}\right)^{\frac{-2}{3}}\\= x^{ -1 . (\frac{-2}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
2. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{2}{3} . (\frac{-1}{6}) }= a^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ a }}=\frac{1}{\sqrt[9]{ a }}. \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a}\\---------------\)
3. \(\left(a^{\frac{1}{2}}\right)^{\frac{5}{3}}\\= a^{ \frac{1}{2} . \frac{5}{3} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
4. \(\left(a^{1}\right)^{\frac{1}{2}}\\= a^{ 1 . \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
5. \(\left(a^{-1}\right)^{-1}\\= a^{ -1 . (-1) }= a^{1}\\\\---------------\)
6. \(\left(a^{\frac{4}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{4}{5} . (\frac{-3}{5}) }= a^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ a^{12} }}=\frac{1}{\sqrt[25]{ a^{12} }}. \color{purple}{\frac{\sqrt[25]{ a^{13} }}{\sqrt[25]{ a^{13} }}} \\=\frac{\sqrt[25]{ a^{13} }}{a}\\---------------\)
7. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-3}{5} . (\frac{-2}{5}) }= q^{\frac{6}{25}}\\=\sqrt[25]{ q^{6} }\\---------------\)
8. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{5}}\\= y^{ \frac{1}{2} . (\frac{-1}{5}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
9. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-1}{2} . (\frac{-1}{5}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
10. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-4}{3} . (\frac{-1}{5}) }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
11. \(\left(a^{2}\right)^{-2}\\= a^{ 2 . (-2) }= a^{-4}\\=\frac{1}{a^{4}}\\---------------\)
12. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{2} . \frac{1}{2} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)