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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{2}}\right)^{1}\\= a^{ \frac{5}{2} . 1 }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
2. \(\left(q^{\frac{3}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{3}{5} . \frac{2}{3} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
3. \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-2}{3} . \frac{1}{3} }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)
4. \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{4}}\\= y^{ \frac{1}{3} . (\frac{-1}{4}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
5. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{3} . (\frac{-1}{2}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
6. \(\left(q^{\frac{-5}{4}}\right)^{-1}\\= q^{ \frac{-5}{4} . (-1) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
7. \(\left(x^{\frac{1}{6}}\right)^{\frac{-4}{5}}\\= x^{ \frac{1}{6} . (\frac{-4}{5}) }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
8. \(\left(y^{\frac{3}{4}}\right)^{\frac{1}{2}}\\= y^{ \frac{3}{4} . \frac{1}{2} }= y^{\frac{3}{8}}\\=\sqrt[8]{ y^{3} }\\---------------\)
9. \(\left(x^{\frac{-3}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-3}{2} . (\frac{-2}{3}) }= x^{1}\\\\---------------\)
10. \(\left(q^{\frac{1}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{1}{5} . \frac{2}{3} }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
11. \(\left(a^{\frac{-1}{4}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{4} . \frac{3}{4} }= a^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ a^{3} }}=\frac{1}{\sqrt[16]{ a^{3} }}. \color{purple}{\frac{\sqrt[16]{ a^{13} }}{\sqrt[16]{ a^{13} }}} \\=\frac{\sqrt[16]{ a^{13} }}{|a|}\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{6}}\\= q^{ \frac{-1}{2} . \frac{1}{6} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)