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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{5}{4}}\right)^{-1}\\= q^{ \frac{5}{4} . (-1) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
2. \(\left(x^{\frac{5}{6}}\right)^{\frac{-1}{4}}\\= x^{ \frac{5}{6} . (\frac{-1}{4}) }= x^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ x^{5} }}=\frac{1}{\sqrt[24]{ x^{5} }}. \color{purple}{\frac{\sqrt[24]{ x^{19} }}{\sqrt[24]{ x^{19} }}} \\=\frac{\sqrt[24]{ x^{19} }}{|x|}\\---------------\)
3. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{2} . \frac{1}{2} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
4. \(\left(q^{\frac{-1}{3}}\right)^{\frac{2}{5}}\\= q^{ \frac{-1}{3} . \frac{2}{5} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
5. \(\left(x^{\frac{-5}{4}}\right)^{\frac{5}{3}}\\= x^{ \frac{-5}{4} . \frac{5}{3} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
6. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-5}{6} . (\frac{-1}{4}) }= x^{\frac{5}{24}}\\=\sqrt[24]{ x^{5} }\\---------------\)
8. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\left(a^{-1}\right)^{\frac{5}{4}}\\= a^{ -1 . \frac{5}{4} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
10. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-2}{3} . (\frac{-5}{2}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
11. \(\left(q^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-2}{3} . \frac{1}{2} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
12. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{5}}\\= x^{ \frac{-1}{3} . \frac{1}{5} }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)