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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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