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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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