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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-4}{5} . (\frac{-1}{4}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
2. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{2}{3} . (\frac{-1}{2}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
3. \(\left(a^{\frac{-1}{2}}\right)^{-1}\\= a^{ \frac{-1}{2} . (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
4. \(\left(a^{-1}\right)^{\frac{2}{5}}\\= a^{ -1 . \frac{2}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
5. \(\left(q^{-1}\right)^{\frac{1}{5}}\\= q^{ -1 . \frac{1}{5} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
6. \(\left(a^{-1}\right)^{-1}\\= a^{ -1 . (-1) }= a^{1}\\\\---------------\)
7. \(\left(q^{\frac{4}{3}}\right)^{\frac{5}{3}}\\= q^{ \frac{4}{3} . \frac{5}{3} }= q^{\frac{20}{9}}\\=\sqrt[9]{ q^{20} }=q^{2}.\sqrt[9]{ q^{2} }\\---------------\)
8. \(\left(x^{\frac{-1}{4}}\right)^{1}\\= x^{ \frac{-1}{4} . 1 }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
9. \(\left(q^{\frac{3}{5}}\right)^{\frac{3}{5}}\\= q^{ \frac{3}{5} . \frac{3}{5} }= q^{\frac{9}{25}}\\=\sqrt[25]{ q^{9} }\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{2}\\= q^{ \frac{1}{2} . 2 }= q^{1}\\\\---------------\)
11. \(\left(q^{\frac{5}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{5}{3} . (\frac{-1}{3}) }= q^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ q^{5} }}=\frac{1}{\sqrt[9]{ q^{5} }}. \color{purple}{\frac{\sqrt[9]{ q^{4} }}{\sqrt[9]{ q^{4} }}} \\=\frac{\sqrt[9]{ q^{4} }}{q}\\---------------\)
12. \(\left(q^{-1}\right)^{\frac{3}{5}}\\= q^{ -1 . \frac{3}{5} }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)