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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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