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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-4}{5}}\right)^{1}\\= x^{ \frac{-4}{5} . 1 }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
2. \(\left(q^{\frac{-3}{4}}\right)^{1}\\= q^{ \frac{-3}{4} . 1 }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
3. \(\left(x^{-1}\right)^{\frac{4}{3}}\\= x^{ -1 . \frac{4}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
4. \(\left(q^{\frac{-2}{5}}\right)^{\frac{2}{5}}\\= q^{ \frac{-2}{5} . \frac{2}{5} }= q^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ q^{4} }}=\frac{1}{\sqrt[25]{ q^{4} }}. \color{purple}{\frac{\sqrt[25]{ q^{21} }}{\sqrt[25]{ q^{21} }}} \\=\frac{\sqrt[25]{ q^{21} }}{q}\\---------------\)
5. \(\left(y^{\frac{-5}{6}}\right)^{\frac{2}{3}}\\= y^{ \frac{-5}{6} . \frac{2}{3} }= y^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ y^{5} }}=\frac{1}{\sqrt[9]{ y^{5} }}. \color{purple}{\frac{\sqrt[9]{ y^{4} }}{\sqrt[9]{ y^{4} }}} \\=\frac{\sqrt[9]{ y^{4} }}{y}\\---------------\)
6. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{2}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
7. \(\left(a^{\frac{-5}{4}}\right)^{\frac{-5}{3}}\\= a^{ \frac{-5}{4} . (\frac{-5}{3}) }= a^{\frac{25}{12}}\\=\sqrt[12]{ a^{25} }=|a^{2}|.\sqrt[12]{ a }\\---------------\)
8. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-1}{2} . (\frac{-3}{4}) }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)
9. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-5}{3} . (\frac{-1}{3}) }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)
10. \(\left(x^{\frac{1}{4}}\right)^{1}\\= x^{ \frac{1}{4} . 1 }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
11. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-2}{3} . (\frac{-5}{3}) }= y^{\frac{10}{9}}\\=\sqrt[9]{ y^{10} }=y.\sqrt[9]{ y }\\---------------\)
12. \(\left(y^{-1}\right)^{\frac{-2}{3}}\\= y^{ -1 . (\frac{-2}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)