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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{6}}\right)^{\frac{-3}{2}}\\= x^{ \frac{5}{6} . (\frac{-3}{2}) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
2. \(\left(x^{\frac{-1}{2}}\right)^{\frac{3}{4}}\\= x^{ \frac{-1}{2} . \frac{3}{4} }= x^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ x^{3} }}=\frac{1}{\sqrt[8]{ x^{3} }}. \color{purple}{\frac{\sqrt[8]{ x^{5} }}{\sqrt[8]{ x^{5} }}} \\=\frac{\sqrt[8]{ x^{5} }}{|x|}\\---------------\)
3. \(\left(x^{\frac{2}{3}}\right)^{\frac{2}{5}}\\= x^{ \frac{2}{3} . \frac{2}{5} }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
4. \(\left(q^{\frac{-1}{3}}\right)^{1}\\= q^{ \frac{-1}{3} . 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
5. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-3}{4} . (\frac{-4}{5}) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
6. \(\left(q^{\frac{-1}{4}}\right)^{\frac{5}{6}}\\= q^{ \frac{-1}{4} . \frac{5}{6} }= q^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ q^{5} }}=\frac{1}{\sqrt[24]{ q^{5} }}. \color{purple}{\frac{\sqrt[24]{ q^{19} }}{\sqrt[24]{ q^{19} }}} \\=\frac{\sqrt[24]{ q^{19} }}{|q|}\\---------------\)
7. \(\left(a^{\frac{-2}{5}}\right)^{\frac{2}{3}}\\= a^{ \frac{-2}{5} . \frac{2}{3} }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
8. \(\left(q^{\frac{5}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{5}{3} . (\frac{-1}{2}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
9. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-2}{3} . (\frac{-2}{3}) }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)
10. \(\left(x^{\frac{4}{5}}\right)^{\frac{5}{3}}\\= x^{ \frac{4}{5} . \frac{5}{3} }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
11. \(\left(y^{\frac{1}{2}}\right)^{1}\\= y^{ \frac{1}{2} . 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
12. \(\left(a^{-2}\right)^{\frac{1}{5}}\\= a^{ -2 . \frac{1}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)