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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{3}}\right)^{\frac{-4}{5}}\\= y^{ \frac{1}{3} . (\frac{-4}{5}) }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
2. \(\left(x^{\frac{5}{4}}\right)^{\frac{-1}{6}}\\= x^{ \frac{5}{4} . (\frac{-1}{6}) }= x^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ x^{5} }}=\frac{1}{\sqrt[24]{ x^{5} }}. \color{purple}{\frac{\sqrt[24]{ x^{19} }}{\sqrt[24]{ x^{19} }}} \\=\frac{\sqrt[24]{ x^{19} }}{|x|}\\---------------\)
3. \(\left(x^{\frac{2}{5}}\right)^{\frac{2}{5}}\\= x^{ \frac{2}{5} . \frac{2}{5} }= x^{\frac{4}{25}}\\=\sqrt[25]{ x^{4} }\\---------------\)
4. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-4}{3}}\\= q^{ \frac{-1}{2} . (\frac{-4}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
5. \(\left(x^{\frac{1}{4}}\right)^{\frac{4}{5}}\\= x^{ \frac{1}{4} . \frac{4}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
6. \(\left(q^{\frac{1}{2}}\right)^{-1}\\= q^{ \frac{1}{2} . (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
7. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
8. \(\left(a^{\frac{-3}{4}}\right)^{\frac{1}{3}}\\= a^{ \frac{-3}{4} . \frac{1}{3} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
9. \(\left(q^{\frac{-3}{2}}\right)^{\frac{1}{4}}\\= q^{ \frac{-3}{2} . \frac{1}{4} }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
10. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{2} . (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
11. \(\left(x^{-1}\right)^{\frac{3}{5}}\\= x^{ -1 . \frac{3}{5} }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
12. \(\left(x^{\frac{2}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{2}{3} . \frac{1}{3} }= x^{\frac{2}{9}}\\=\sqrt[9]{ x^{2} }\\---------------\)