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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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