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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-3}{4} . (\frac{-3}{2}) }= a^{\frac{9}{8}}\\=\sqrt[8]{ a^{9} }=|a|.\sqrt[8]{ a }\\---------------\)
2. \(\left(q^{\frac{1}{5}}\right)^{\frac{-2}{3}}\\= q^{ \frac{1}{5} . (\frac{-2}{3}) }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
3. \(\left(a^{\frac{-2}{5}}\right)^{\frac{1}{2}}\\= a^{ \frac{-2}{5} . \frac{1}{2} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
4. \(\left(q^{\frac{5}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{5}{2} . \frac{1}{3} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
5. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-2}{5} . (\frac{-1}{3}) }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
6. \(\left(x^{\frac{-5}{3}}\right)^{\frac{5}{4}}\\= x^{ \frac{-5}{3} . \frac{5}{4} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
7. \(\left(a^{\frac{5}{6}}\right)^{-1}\\= a^{ \frac{5}{6} . (-1) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
8. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-1}{3} . (\frac{-2}{3}) }= x^{\frac{2}{9}}\\=\sqrt[9]{ x^{2} }\\---------------\)
9. \(\left(a^{\frac{-1}{2}}\right)^{-1}\\= a^{ \frac{-1}{2} . (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
10. \(\left(a^{\frac{3}{2}}\right)^{\frac{-3}{2}}\\= a^{ \frac{3}{2} . (\frac{-3}{2}) }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
11. \(\left(y^{\frac{1}{4}}\right)^{\frac{-1}{5}}\\= y^{ \frac{1}{4} . (\frac{-1}{5}) }= y^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ y }}=\frac{1}{\sqrt[20]{ y }}. \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y|}\\---------------\)
12. \(\left(q^{\frac{-5}{2}}\right)^{-1}\\= q^{ \frac{-5}{2} . (-1) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)