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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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