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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{1}\right)^{\frac{5}{6}}\\= a^{ 1 . \frac{5}{6} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
2. \(\left(a^{\frac{3}{4}}\right)^{\frac{3}{2}}\\= a^{ \frac{3}{4} . \frac{3}{2} }= a^{\frac{9}{8}}\\=\sqrt[8]{ a^{9} }=|a|.\sqrt[8]{ a }\\---------------\)
3. \(\left(x^{\frac{1}{6}}\right)^{\frac{3}{4}}\\= x^{ \frac{1}{6} . \frac{3}{4} }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
4. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{5}}\\= a^{ \frac{1}{3} . (\frac{-1}{5}) }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
5. \(\left(q^{\frac{3}{4}}\right)^{-1}\\= q^{ \frac{3}{4} . (-1) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
6. \(\left(q^{\frac{-3}{4}}\right)^{\frac{5}{6}}\\= q^{ \frac{-3}{4} . \frac{5}{6} }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{3}{4}}\\= a^{ -1 . \frac{3}{4} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
8. \(\left(a^{-1}\right)^{\frac{1}{5}}\\= a^{ -1 . \frac{1}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
9. \(\left(a^{\frac{1}{2}}\right)^{\frac{5}{3}}\\= a^{ \frac{1}{2} . \frac{5}{3} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
10. \(\left(x^{\frac{4}{5}}\right)^{\frac{1}{3}}\\= x^{ \frac{4}{5} . \frac{1}{3} }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
11. \(\left(x^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= x^{ \frac{1}{2} . \frac{1}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
12. \(\left(q^{\frac{-3}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-3}{2} . (\frac{-3}{4}) }= q^{\frac{9}{8}}\\=\sqrt[8]{ q^{9} }=|q|.\sqrt[8]{ q }\\---------------\)