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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{4}}\right)^{\frac{1}{5}}\\= q^{ \frac{1}{4} . \frac{1}{5} }= q^{\frac{1}{20}}\\=\sqrt[20]{ q }\\---------------\)
2. \(\left(q^{\frac{-1}{4}}\right)^{\frac{4}{3}}\\= q^{ \frac{-1}{4} . \frac{4}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
3. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-3}{5} . (\frac{-3}{2}) }= q^{\frac{9}{10}}\\=\sqrt[10]{ q^{9} }\\---------------\)
4. \(\left(q^{1}\right)^{\frac{-5}{3}}\\= q^{ 1 . (\frac{-5}{3}) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
5. \(\left(y^{\frac{-5}{3}}\right)^{-1}\\= y^{ \frac{-5}{3} . (-1) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
6. \(\left(q^{\frac{-5}{4}}\right)^{-1}\\= q^{ \frac{-5}{4} . (-1) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
7. \(\left(x^{\frac{3}{5}}\right)^{\frac{-1}{6}}\\= x^{ \frac{3}{5} . (\frac{-1}{6}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
8. \(\left(a^{\frac{-2}{3}}\right)^{\frac{3}{5}}\\= a^{ \frac{-2}{3} . \frac{3}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
9. \(\left(q^{\frac{1}{3}}\right)^{\frac{3}{2}}\\= q^{ \frac{1}{3} . \frac{3}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(\left(a^{\frac{2}{3}}\right)^{1}\\= a^{ \frac{2}{3} . 1 }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
11. \(\left(x^{\frac{-5}{4}}\right)^{\frac{5}{2}}\\= x^{ \frac{-5}{4} . \frac{5}{2} }= x^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ x^{25} }}\\=\frac{1}{|x^{3}|.\sqrt[8]{ x }}=\frac{1}{|x^{3}|.\sqrt[8]{ x }} \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x^{4}|}\\---------------\)
12. \(\left(x^{\frac{-5}{6}}\right)^{1}\\= x^{ \frac{-5}{6} . 1 }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)