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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-3}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-3}{2} . (\frac{-1}{2}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
2. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-1}{5} . (\frac{-4}{5}) }= a^{\frac{4}{25}}\\=\sqrt[25]{ a^{4} }\\---------------\)
3. \(\left(a^{\frac{-5}{3}}\right)^{1}\\= a^{ \frac{-5}{3} . 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
4. \(\left(x^{-1}\right)^{-1}\\= x^{ -1 . (-1) }= x^{1}\\\\---------------\)
5. \(\left(y^{-2}\right)^{-1}\\= y^{ -2 . (-1) }= y^{2}\\\\---------------\)
6. \(\left(a^{\frac{-1}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-1}{3} . \frac{1}{3} }= a^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ a }}=\frac{1}{\sqrt[9]{ a }}. \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a}\\---------------\)
7. \(\left(a^{\frac{5}{4}}\right)^{\frac{3}{5}}\\= a^{ \frac{5}{4} . \frac{3}{5} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
8. \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{5}}\\= y^{ \frac{1}{3} . (\frac{-1}{5}) }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
9. \(\left(q^{-1}\right)^{1}\\= q^{ -1 . 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)
10. \(\left(x^{-1}\right)^{\frac{-1}{3}}\\= x^{ -1 . (\frac{-1}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
11. \(\left(a^{\frac{4}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{4}{5} . \frac{1}{3} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
12. \(\left(a^{\frac{-1}{5}}\right)^{\frac{1}{5}}\\= a^{ \frac{-1}{5} . \frac{1}{5} }= a^{\frac{-1}{25}}\\=\frac{1}{\sqrt[25]{ a }}=\frac{1}{\sqrt[25]{ a }}. \color{purple}{\frac{\sqrt[25]{ a^{24} }}{\sqrt[25]{ a^{24} }}} \\=\frac{\sqrt[25]{ a^{24} }}{a}\\---------------\)