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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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