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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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