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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{2}\right)^{\frac{5}{3}}\\= q^{ 2 . \frac{5}{3} }= q^{\frac{10}{3}}\\=\sqrt[3]{ q^{10} }=q^{3}.\sqrt[3]{ q }\\---------------\)
2. \(\left(a^{\frac{3}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{3}{4} . \frac{1}{2} }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)
3. \(\left(x^{-2}\right)^{\frac{1}{6}}\\= x^{ -2 . \frac{1}{6} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
4. \(\left(y^{-1}\right)^{\frac{-2}{5}}\\= y^{ -1 . (\frac{-2}{5}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
5. \(\left(a^{\frac{-1}{3}}\right)^{\frac{5}{4}}\\= a^{ \frac{-1}{3} . \frac{5}{4} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
6. \(\left(x^{\frac{3}{2}}\right)^{\frac{1}{4}}\\= x^{ \frac{3}{2} . \frac{1}{4} }= x^{\frac{3}{8}}\\=\sqrt[8]{ x^{3} }\\---------------\)
7. \(\left(a^{\frac{-1}{6}}\right)^{\frac{1}{3}}\\= a^{ \frac{-1}{6} . \frac{1}{3} }= a^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ a }}=\frac{1}{\sqrt[18]{ a }}. \color{purple}{\frac{\sqrt[18]{ a^{17} }}{\sqrt[18]{ a^{17} }}} \\=\frac{\sqrt[18]{ a^{17} }}{|a|}\\---------------\)
8. \(\left(a^{\frac{-2}{3}}\right)^{-1}\\= a^{ \frac{-2}{3} . (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
9. \(\left(y^{\frac{1}{5}}\right)^{\frac{5}{4}}\\= y^{ \frac{1}{5} . \frac{5}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
10. \(\left(q^{\frac{-1}{6}}\right)^{-2}\\= q^{ \frac{-1}{6} . (-2) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
11. \(\left(x^{\frac{4}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{4}{5} . \frac{1}{2} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
12. \(\left(a^{\frac{5}{2}}\right)^{\frac{1}{3}}\\= a^{ \frac{5}{2} . \frac{1}{3} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)