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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-3}{5}}\right)^{\frac{3}{2}}\\= x^{ \frac{-3}{5} . \frac{3}{2} }= x^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ x^{9} }}=\frac{1}{\sqrt[10]{ x^{9} }}. \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x|}\\---------------\)
2. \(\left(x^{\frac{5}{3}}\right)^{\frac{-1}{6}}\\= x^{ \frac{5}{3} . (\frac{-1}{6}) }= x^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ x^{5} }}=\frac{1}{\sqrt[18]{ x^{5} }}. \color{purple}{\frac{\sqrt[18]{ x^{13} }}{\sqrt[18]{ x^{13} }}} \\=\frac{\sqrt[18]{ x^{13} }}{|x|}\\---------------\)
3. \(\left(q^{\frac{-4}{5}}\right)^{\frac{2}{5}}\\= q^{ \frac{-4}{5} . \frac{2}{5} }= q^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ q^{8} }}=\frac{1}{\sqrt[25]{ q^{8} }}. \color{purple}{\frac{\sqrt[25]{ q^{17} }}{\sqrt[25]{ q^{17} }}} \\=\frac{\sqrt[25]{ q^{17} }}{q}\\---------------\)
4. \(\left(q^{\frac{3}{2}}\right)^{\frac{-5}{3}}\\= q^{ \frac{3}{2} . (\frac{-5}{3}) }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
5. \(\left(q^{-2}\right)^{\frac{-1}{3}}\\= q^{ -2 . (\frac{-1}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
6. \(\left(a^{\frac{-2}{5}}\right)^{\frac{1}{6}}\\= a^{ \frac{-2}{5} . \frac{1}{6} }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
7. \(\left(x^{\frac{-1}{6}}\right)^{\frac{2}{5}}\\= x^{ \frac{-1}{6} . \frac{2}{5} }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
8. \(\left(a^{\frac{1}{3}}\right)^{\frac{-5}{4}}\\= a^{ \frac{1}{3} . (\frac{-5}{4}) }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
9. \(\left(y^{\frac{5}{3}}\right)^{\frac{4}{3}}\\= y^{ \frac{5}{3} . \frac{4}{3} }= y^{\frac{20}{9}}\\=\sqrt[9]{ y^{20} }=y^{2}.\sqrt[9]{ y^{2} }\\---------------\)
10. \(\left(y^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{2} . \frac{2}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
11. \(\left(x^{\frac{3}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{3}{5} . \frac{1}{2} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
12. \(\left(x^{\frac{3}{4}}\right)^{\frac{-2}{5}}\\= x^{ \frac{3}{4} . (\frac{-2}{5}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)