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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{4}{3}}\right)^{\frac{-1}{5}}\\= a^{ \frac{4}{3} . (\frac{-1}{5}) }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
2. \(\left(q^{\frac{5}{6}}\right)^{\frac{4}{5}}\\= q^{ \frac{5}{6} . \frac{4}{5} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
3. \(\left(q^{\frac{-2}{5}}\right)^{1}\\= q^{ \frac{-2}{5} . 1 }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
4. \(\left(y^{-1}\right)^{\frac{1}{4}}\\= y^{ -1 . \frac{1}{4} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
5. \(\left(x^{\frac{4}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{4}{3} . (\frac{-2}{3}) }= x^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ x^{8} }}=\frac{1}{\sqrt[9]{ x^{8} }}. \color{purple}{\frac{\sqrt[9]{ x }}{\sqrt[9]{ x }}} \\=\frac{\sqrt[9]{ x }}{x}\\---------------\)
6. \(\left(x^{-1}\right)^{\frac{1}{3}}\\= x^{ -1 . \frac{1}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
7. \(\left(y^{\frac{3}{4}}\right)^{\frac{5}{6}}\\= y^{ \frac{3}{4} . \frac{5}{6} }= y^{\frac{5}{8}}\\=\sqrt[8]{ y^{5} }\\---------------\)
8. \(\left(q^{1}\right)^{\frac{-3}{5}}\\= q^{ 1 . (\frac{-3}{5}) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
9. \(\left(x^{\frac{1}{6}}\right)^{\frac{-1}{3}}\\= x^{ \frac{1}{6} . (\frac{-1}{3}) }= x^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ x }}=\frac{1}{\sqrt[18]{ x }}. \color{purple}{\frac{\sqrt[18]{ x^{17} }}{\sqrt[18]{ x^{17} }}} \\=\frac{\sqrt[18]{ x^{17} }}{|x|}\\---------------\)
10. \(\left(y^{2}\right)^{\frac{1}{2}}\\= y^{ 2 . \frac{1}{2} }= y^{1}\\\\---------------\)
11. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-4}{3}}\\= y^{ \frac{-5}{2} . (\frac{-4}{3}) }= y^{\frac{10}{3}}\\=\sqrt[3]{ y^{10} }=y^{3}.\sqrt[3]{ y }\\---------------\)
12. \(\left(x^{\frac{2}{5}}\right)^{\frac{-2}{3}}\\= x^{ \frac{2}{5} . (\frac{-2}{3}) }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)