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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-2}{5}}\right)^{\frac{2}{5}}\\= y^{ \frac{-2}{5} . \frac{2}{5} }= y^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ y^{4} }}=\frac{1}{\sqrt[25]{ y^{4} }}. \color{purple}{\frac{\sqrt[25]{ y^{21} }}{\sqrt[25]{ y^{21} }}} \\=\frac{\sqrt[25]{ y^{21} }}{y}\\---------------\)
2. \(\left(a^{\frac{-5}{4}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-5}{4} . (\frac{-5}{2}) }= a^{\frac{25}{8}}\\=\sqrt[8]{ a^{25} }=|a^{3}|.\sqrt[8]{ a }\\---------------\)
3. \(\left(y^{\frac{-4}{5}}\right)^{\frac{5}{4}}\\= y^{ \frac{-4}{5} . \frac{5}{4} }= y^{-1}\\=\frac{1}{y}\\---------------\)
4. \(\left(a^{\frac{-4}{5}}\right)^{\frac{1}{4}}\\= a^{ \frac{-4}{5} . \frac{1}{4} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
5. \(\left(a^{\frac{1}{3}}\right)^{-1}\\= a^{ \frac{1}{3} . (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
6. \(\left(q^{\frac{-3}{4}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-3}{4} . (\frac{-1}{6}) }= q^{\frac{1}{8}}\\=\sqrt[8]{ q }\\---------------\)
7. \(\left(q^{\frac{4}{5}}\right)^{\frac{4}{3}}\\= q^{ \frac{4}{5} . \frac{4}{3} }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
8. \(\left(a^{-1}\right)^{1}\\= a^{ -1 . 1 }= a^{-1}\\=\frac{1}{a}\\---------------\)
9. \(\left(x^{\frac{5}{4}}\right)^{\frac{5}{2}}\\= x^{ \frac{5}{4} . \frac{5}{2} }= x^{\frac{25}{8}}\\=\sqrt[8]{ x^{25} }=|x^{3}|.\sqrt[8]{ x }\\---------------\)
10. \(\left(a^{1}\right)^{1}\\= a^{ 1 . 1 }= a^{1}\\\\---------------\)
11. \(\left(a^{\frac{2}{3}}\right)^{\frac{-3}{2}}\\= a^{ \frac{2}{3} . (\frac{-3}{2}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
12. \(\left(a^{1}\right)^{\frac{1}{3}}\\= a^{ 1 . \frac{1}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)