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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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