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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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