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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{2}}\\= a^{ \frac{5}{6} . \frac{1}{2} }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
2. \(\left(a^{\frac{-5}{6}}\right)^{\frac{2}{3}}\\= a^{ \frac{-5}{6} . \frac{2}{3} }= a^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ a^{5} }}=\frac{1}{\sqrt[9]{ a^{5} }}. \color{purple}{\frac{\sqrt[9]{ a^{4} }}{\sqrt[9]{ a^{4} }}} \\=\frac{\sqrt[9]{ a^{4} }}{a}\\---------------\)
3. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-3}{4} . (\frac{-5}{2}) }= a^{\frac{15}{8}}\\=\sqrt[8]{ a^{15} }=|a|.\sqrt[8]{ a^{7} }\\---------------\)
4. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-1}{3} . (\frac{-5}{4}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
5. \(\left(x^{\frac{-1}{4}}\right)^{\frac{4}{3}}\\= x^{ \frac{-1}{4} . \frac{4}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\left(x^{\frac{-1}{6}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-1}{6} . (\frac{-1}{6}) }= x^{\frac{1}{36}}\\=\sqrt[36]{ x }\\---------------\)
7. \(\left(q^{\frac{1}{2}}\right)^{\frac{4}{3}}\\= q^{ \frac{1}{2} . \frac{4}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
8. \(\left(x^{1}\right)^{\frac{-4}{3}}\\= x^{ 1 . (\frac{-4}{3}) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
9. \(\left(q^{\frac{5}{3}}\right)^{-1}\\= q^{ \frac{5}{3} . (-1) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
10. \(\left(a^{\frac{1}{3}}\right)^{2}\\= a^{ \frac{1}{3} . 2 }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
11. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-1}{2} . (\frac{-5}{2}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{6}}\\= q^{ \frac{-1}{2} . \frac{1}{6} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)