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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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