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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{3}{4}}\right)^{\frac{-3}{4}}\\= q^{ \frac{3}{4} . (\frac{-3}{4}) }= q^{\frac{-9}{16}}\\=\frac{1}{\sqrt[16]{ q^{9} }}=\frac{1}{\sqrt[16]{ q^{9} }}. \color{purple}{\frac{\sqrt[16]{ q^{7} }}{\sqrt[16]{ q^{7} }}} \\=\frac{\sqrt[16]{ q^{7} }}{|q|}\\---------------\)
2. \(\left(q^{\frac{5}{6}}\right)^{-1}\\= q^{ \frac{5}{6} . (-1) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
3. \(\left(q^{\frac{2}{5}}\right)^{\frac{1}{5}}\\= q^{ \frac{2}{5} . \frac{1}{5} }= q^{\frac{2}{25}}\\=\sqrt[25]{ q^{2} }\\---------------\)
4. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{4}}\\= a^{ \frac{1}{2} . (\frac{-1}{4}) }= a^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ a }}=\frac{1}{\sqrt[8]{ a }}. \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a|}\\---------------\)
5. \(\left(q^{\frac{-5}{3}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-5}{3} . (\frac{-2}{3}) }= q^{\frac{10}{9}}\\=\sqrt[9]{ q^{10} }=q.\sqrt[9]{ q }\\---------------\)
6. \(\left(a^{\frac{-4}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-4}{3} . \frac{2}{3} }= a^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ a^{8} }}=\frac{1}{\sqrt[9]{ a^{8} }}. \color{purple}{\frac{\sqrt[9]{ a }}{\sqrt[9]{ a }}} \\=\frac{\sqrt[9]{ a }}{a}\\---------------\)
7. \(\left(x^{-1}\right)^{\frac{-2}{3}}\\= x^{ -1 . (\frac{-2}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
8. \(\left(x^{\frac{3}{2}}\right)^{\frac{1}{5}}\\= x^{ \frac{3}{2} . \frac{1}{5} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
9. \(\left(x^{\frac{2}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{2}{5} . \frac{1}{2} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
10. \(\left(a^{\frac{1}{6}}\right)^{\frac{-4}{5}}\\= a^{ \frac{1}{6} . (\frac{-4}{5}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
11. \(\left(a^{1}\right)^{\frac{-5}{4}}\\= a^{ 1 . (\frac{-5}{4}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
12. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-1}{5}}\\= a^{ \frac{-4}{3} . (\frac{-1}{5}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)