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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{3}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{3}{5} . \frac{2}{3} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
2. \(\left(a^{\frac{-1}{4}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-1}{4} . (\frac{-4}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
3. \(\left(x^{1}\right)^{\frac{-3}{2}}\\= x^{ 1 . (\frac{-3}{2}) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
4. \(\left(q^{\frac{3}{4}}\right)^{-2}\\= q^{ \frac{3}{4} . (-2) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
5. \(\left(q^{\frac{1}{5}}\right)^{\frac{4}{3}}\\= q^{ \frac{1}{5} . \frac{4}{3} }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
6. \(\left(q^{\frac{4}{5}}\right)^{1}\\= q^{ \frac{4}{5} . 1 }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
7. \(\left(y^{\frac{-3}{5}}\right)^{\frac{2}{5}}\\= y^{ \frac{-3}{5} . \frac{2}{5} }= y^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ y^{6} }}=\frac{1}{\sqrt[25]{ y^{6} }}. \color{purple}{\frac{\sqrt[25]{ y^{19} }}{\sqrt[25]{ y^{19} }}} \\=\frac{\sqrt[25]{ y^{19} }}{y}\\---------------\)
8. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{3}}\\= a^{ \frac{5}{6} . \frac{1}{3} }= a^{\frac{5}{18}}\\=\sqrt[18]{ a^{5} }\\---------------\)
9. \(\left(q^{2}\right)^{\frac{2}{3}}\\= q^{ 2 . \frac{2}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
10. \(\left(q^{\frac{3}{4}}\right)^{-1}\\= q^{ \frac{3}{4} . (-1) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
11. \(\left(x^{\frac{4}{3}}\right)^{-1}\\= x^{ \frac{4}{3} . (-1) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
12. \(\left(a^{\frac{-1}{6}}\right)^{\frac{1}{5}}\\= a^{ \frac{-1}{6} . \frac{1}{5} }= a^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ a }}=\frac{1}{\sqrt[30]{ a }}. \color{purple}{\frac{\sqrt[30]{ a^{29} }}{\sqrt[30]{ a^{29} }}} \\=\frac{\sqrt[30]{ a^{29} }}{|a|}\\---------------\)