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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-2}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{-2}{3} . \frac{1}{3} }= y^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ y^{2} }}=\frac{1}{\sqrt[9]{ y^{2} }}. \color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y}\\---------------\)
2. \(\left(a^{\frac{-3}{5}}\right)^{\frac{1}{6}}\\= a^{ \frac{-3}{5} . \frac{1}{6} }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
3. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-3}{2}}\\= y^{ \frac{-3}{5} . (\frac{-3}{2}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
4. \(\left(a^{\frac{-3}{4}}\right)^{\frac{2}{5}}\\= a^{ \frac{-3}{4} . \frac{2}{5} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
5. \(\left(q^{\frac{3}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{3}{5} . \frac{2}{3} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
6. \(\left(y^{\frac{3}{4}}\right)^{-1}\\= y^{ \frac{3}{4} . (-1) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
7. \(\left(q^{\frac{5}{4}}\right)^{\frac{-5}{6}}\\= q^{ \frac{5}{4} . (\frac{-5}{6}) }= q^{\frac{-25}{24}}\\=\frac{1}{\sqrt[24]{ q^{25} }}\\=\frac{1}{|q|.\sqrt[24]{ q }}=\frac{1}{|q|.\sqrt[24]{ q }} \color{purple}{\frac{\sqrt[24]{ q^{23} }}{\sqrt[24]{ q^{23} }}} \\=\frac{\sqrt[24]{ q^{23} }}{|q^{2}|}\\---------------\)
8. \(\left(y^{-1}\right)^{\frac{-1}{2}}\\= y^{ -1 . (\frac{-1}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
9. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-2}{5} . (\frac{-1}{6}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
10. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-4}{3} . (\frac{-1}{6}) }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)
11. \(\left(q^{1}\right)^{-2}\\= q^{ 1 . (-2) }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
12. \(\left(x^{\frac{-5}{3}}\right)^{2}\\= x^{ \frac{-5}{3} . 2 }= x^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ x^{10} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x }}=\frac{1}{x^{3}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{4}}\\---------------\)