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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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