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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{3}}\right)^{\frac{3}{2}}\\= a^{ \frac{1}{3} . \frac{3}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
2. \(\left(a^{\frac{4}{5}}\right)^{\frac{1}{5}}\\= a^{ \frac{4}{5} . \frac{1}{5} }= a^{\frac{4}{25}}\\=\sqrt[25]{ a^{4} }\\---------------\)
3. \(\left(q^{\frac{4}{5}}\right)^{\frac{-2}{3}}\\= q^{ \frac{4}{5} . (\frac{-2}{3}) }= q^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ q^{8} }}=\frac{1}{\sqrt[15]{ q^{8} }}. \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q}\\---------------\)
4. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-1}{2} . (\frac{-5}{3}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
5. \(\left(q^{\frac{3}{5}}\right)^{\frac{-3}{5}}\\= q^{ \frac{3}{5} . (\frac{-3}{5}) }= q^{\frac{-9}{25}}\\=\frac{1}{\sqrt[25]{ q^{9} }}=\frac{1}{\sqrt[25]{ q^{9} }}. \color{purple}{\frac{\sqrt[25]{ q^{16} }}{\sqrt[25]{ q^{16} }}} \\=\frac{\sqrt[25]{ q^{16} }}{q}\\---------------\)
6. \(\left(x^{\frac{3}{2}}\right)^{\frac{-1}{6}}\\= x^{ \frac{3}{2} . (\frac{-1}{6}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
7. \(\left(y^{1}\right)^{\frac{-1}{4}}\\= y^{ 1 . (\frac{-1}{4}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
8. \(\left(q^{\frac{1}{4}}\right)^{-1}\\= q^{ \frac{1}{4} . (-1) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
9. \(\left(y^{\frac{-1}{6}}\right)^{\frac{5}{3}}\\= y^{ \frac{-1}{6} . \frac{5}{3} }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
10. \(\left(q^{1}\right)^{\frac{5}{4}}\\= q^{ 1 . \frac{5}{4} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
11. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-2}{5} . (\frac{-1}{3}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
12. \(\left(q^{1}\right)^{\frac{2}{5}}\\= q^{ 1 . \frac{2}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)