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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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