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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{4}{5}}\right)^{1}\\= q^{ \frac{4}{5} . 1 }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
2. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-3}{5} . (\frac{-3}{4}) }= q^{\frac{9}{20}}\\=\sqrt[20]{ q^{9} }\\---------------\)
3. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-2}{5} . (\frac{-1}{3}) }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
4. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-5}{6}}\\= q^{ \frac{-5}{6} . (\frac{-5}{6}) }= q^{\frac{25}{36}}\\=\sqrt[36]{ q^{25} }\\---------------\)
5. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-3}{4}}\\= x^{ \frac{-4}{5} . (\frac{-3}{4}) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
6. \(\left(x^{-1}\right)^{1}\\= x^{ -1 . 1 }= x^{-1}\\=\frac{1}{x}\\---------------\)
7. \(\left(x^{\frac{-5}{6}}\right)^{\frac{2}{3}}\\= x^{ \frac{-5}{6} . \frac{2}{3} }= x^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ x^{5} }}=\frac{1}{\sqrt[9]{ x^{5} }}. \color{purple}{\frac{\sqrt[9]{ x^{4} }}{\sqrt[9]{ x^{4} }}} \\=\frac{\sqrt[9]{ x^{4} }}{x}\\---------------\)
8. \(\left(a^{\frac{-1}{3}}\right)^{\frac{3}{5}}\\= a^{ \frac{-1}{3} . \frac{3}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
9. \(\left(x^{\frac{-5}{2}}\right)^{\frac{2}{5}}\\= x^{ \frac{-5}{2} . \frac{2}{5} }= x^{-1}\\=\frac{1}{x}\\---------------\)
10. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-1}{3} . (\frac{-5}{6}) }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)
11. \(\left(q^{\frac{4}{5}}\right)^{-1}\\= q^{ \frac{4}{5} . (-1) }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
12. \(\left(y^{\frac{1}{4}}\right)^{\frac{1}{4}}\\= y^{ \frac{1}{4} . \frac{1}{4} }= y^{\frac{1}{16}}\\=\sqrt[16]{ y }\\---------------\)