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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-3}{5}}\right)^{\frac{4}{3}}\\= y^{ \frac{-3}{5} . \frac{4}{3} }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
2. \(\left(q^{1}\right)^{\frac{2}{5}}\\= q^{ 1 . \frac{2}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
3. \(\left(y^{\frac{-5}{4}}\right)^{-2}\\= y^{ \frac{-5}{4} . (-2) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
4. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-1}{5}}\\= a^{ \frac{-1}{2} . (\frac{-1}{5}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
5. \(\left(x^{\frac{-3}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-3}{2} . (\frac{-1}{2}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
6. \(\left(a^{\frac{3}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{3}{4} . \frac{1}{2} }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)
7. \(\left(x^{-1}\right)^{1}\\= x^{ -1 . 1 }= x^{-1}\\=\frac{1}{x}\\---------------\)
8. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-5}{4} . (\frac{-5}{4}) }= q^{\frac{25}{16}}\\=\sqrt[16]{ q^{25} }=|q|.\sqrt[16]{ q^{9} }\\---------------\)
9. \(\left(y^{\frac{-2}{3}}\right)^{\frac{3}{2}}\\= y^{ \frac{-2}{3} . \frac{3}{2} }= y^{-1}\\=\frac{1}{y}\\---------------\)
10. \(\left(a^{-1}\right)^{\frac{-1}{5}}\\= a^{ -1 . (\frac{-1}{5}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
11. \(\left(y^{\frac{-1}{5}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{5} . \frac{2}{3} }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
12. \(\left(a^{-2}\right)^{\frac{-5}{2}}\\= a^{ -2 . (\frac{-5}{2}) }= a^{5}\\\\---------------\)