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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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