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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-2}{5} . (\frac{-1}{2}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
2. \(\left(a^{\frac{-5}{3}}\right)^{-1}\\= a^{ \frac{-5}{3} . (-1) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-1}{3} . (\frac{-4}{5}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
4. \(\left(y^{-1}\right)^{\frac{-1}{5}}\\= y^{ -1 . (\frac{-1}{5}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
5. \(\left(q^{\frac{5}{3}}\right)^{\frac{1}{3}}\\= q^{ \frac{5}{3} . \frac{1}{3} }= q^{\frac{5}{9}}\\=\sqrt[9]{ q^{5} }\\---------------\)
6. \(\left(a^{\frac{1}{4}}\right)^{\frac{1}{6}}\\= a^{ \frac{1}{4} . \frac{1}{6} }= a^{\frac{1}{24}}\\=\sqrt[24]{ a }\\---------------\)
7. \(\left(x^{-1}\right)^{-2}\\= x^{ -1 . (-2) }= x^{2}\\\\---------------\)
8. \(\left(q^{\frac{3}{5}}\right)^{\frac{-3}{4}}\\= q^{ \frac{3}{5} . (\frac{-3}{4}) }= q^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ q^{9} }}=\frac{1}{\sqrt[20]{ q^{9} }}. \color{purple}{\frac{\sqrt[20]{ q^{11} }}{\sqrt[20]{ q^{11} }}} \\=\frac{\sqrt[20]{ q^{11} }}{|q|}\\---------------\)
9. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{3} . \frac{1}{2} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
10. \(\left(a^{\frac{4}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{4}{5} . (\frac{-1}{2}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
11. \(\left(y^{\frac{-3}{5}}\right)^{\frac{2}{3}}\\= y^{ \frac{-3}{5} . \frac{2}{3} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
12. \(\left(q^{-2}\right)^{\frac{-2}{3}}\\= q^{ -2 . (\frac{-2}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)