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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{-1}\right)^{\frac{3}{4}}\\= x^{ -1 . \frac{3}{4} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
2. \(\left(q^{-1}\right)^{\frac{-3}{4}}\\= q^{ -1 . (\frac{-3}{4}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
3. \(\left(q^{\frac{5}{6}}\right)^{\frac{5}{2}}\\= q^{ \frac{5}{6} . \frac{5}{2} }= q^{\frac{25}{12}}\\=\sqrt[12]{ q^{25} }=|q^{2}|.\sqrt[12]{ q }\\---------------\)
4. \(\left(a^{\frac{1}{3}}\right)^{-1}\\= a^{ \frac{1}{3} . (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\left(q^{-1}\right)^{\frac{-2}{3}}\\= q^{ -1 . (\frac{-2}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
6. \(\left(a^{\frac{2}{3}}\right)^{\frac{5}{3}}\\= a^{ \frac{2}{3} . \frac{5}{3} }= a^{\frac{10}{9}}\\=\sqrt[9]{ a^{10} }=a.\sqrt[9]{ a }\\---------------\)
7. \(\left(x^{\frac{-1}{6}}\right)^{\frac{3}{5}}\\= x^{ \frac{-1}{6} . \frac{3}{5} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
8. \(\left(y^{1}\right)^{\frac{2}{5}}\\= y^{ 1 . \frac{2}{5} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
9. \(\left(a^{\frac{5}{2}}\right)^{\frac{-3}{2}}\\= a^{ \frac{5}{2} . (\frac{-3}{2}) }= a^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ a^{15} }}\\=\frac{1}{|a^{3}|.\sqrt[4]{ a^{3} }}=\frac{1}{|a^{3}|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{4}|}\\---------------\)
10. \(\left(x^{\frac{1}{2}}\right)^{\frac{1}{6}}\\= x^{ \frac{1}{2} . \frac{1}{6} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
11. \(\left(a^{\frac{-1}{5}}\right)^{\frac{1}{4}}\\= a^{ \frac{-1}{5} . \frac{1}{4} }= a^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ a }}=\frac{1}{\sqrt[20]{ a }}. \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a|}\\---------------\)
12. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-5}{3}}\\= a^{ \frac{-4}{5} . (\frac{-5}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)