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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{4}}\right)^{\frac{-3}{5}}\\= x^{ \frac{1}{4} . (\frac{-3}{5}) }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)
2. \(\left(y^{\frac{-5}{6}}\right)^{1}\\= y^{ \frac{-5}{6} . 1 }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
3. \(\left(a^{\frac{-3}{4}}\right)^{-1}\\= a^{ \frac{-3}{4} . (-1) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
4. \(\left(y^{\frac{3}{2}}\right)^{\frac{-4}{3}}\\= y^{ \frac{3}{2} . (\frac{-4}{3}) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
5. \(\left(x^{\frac{-2}{3}}\right)^{\frac{5}{2}}\\= x^{ \frac{-2}{3} . \frac{5}{2} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
6. \(\left(x^{\frac{4}{3}}\right)^{\frac{4}{5}}\\= x^{ \frac{4}{3} . \frac{4}{5} }= x^{\frac{16}{15}}\\=\sqrt[15]{ x^{16} }=x.\sqrt[15]{ x }\\---------------\)
7. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-4}{3} . (\frac{-5}{2}) }= a^{\frac{10}{3}}\\=\sqrt[3]{ a^{10} }=a^{3}.\sqrt[3]{ a }\\---------------\)
8. \(\left(q^{\frac{3}{4}}\right)^{\frac{1}{3}}\\= q^{ \frac{3}{4} . \frac{1}{3} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
9. \(\left(q^{\frac{-5}{3}}\right)^{\frac{2}{5}}\\= q^{ \frac{-5}{3} . \frac{2}{5} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
10. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-4}{5} . (\frac{-5}{6}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
11. \(\left(x^{-2}\right)^{\frac{5}{2}}\\= x^{ -2 . \frac{5}{2} }= x^{-5}\\=\frac{1}{x^{5}}\\---------------\)
12. \(\left(y^{-1}\right)^{\frac{1}{4}}\\= y^{ -1 . \frac{1}{4} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)