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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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