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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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