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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-4}{5} . (\frac{-5}{4}) }= x^{1}\\\\---------------\)
2. \(\left(y^{-1}\right)^{\frac{-2}{3}}\\= y^{ -1 . (\frac{-2}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
3. \(\left(y^{\frac{1}{5}}\right)^{\frac{-1}{6}}\\= y^{ \frac{1}{5} . (\frac{-1}{6}) }= y^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ y }}=\frac{1}{\sqrt[30]{ y }}. \color{purple}{\frac{\sqrt[30]{ y^{29} }}{\sqrt[30]{ y^{29} }}} \\=\frac{\sqrt[30]{ y^{29} }}{|y|}\\---------------\)
4. \(\left(a^{\frac{-4}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-4}{3} . \frac{2}{3} }= a^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ a^{8} }}=\frac{1}{\sqrt[9]{ a^{8} }}. \color{purple}{\frac{\sqrt[9]{ a }}{\sqrt[9]{ a }}} \\=\frac{\sqrt[9]{ a }}{a}\\---------------\)
5. \(\left(y^{\frac{5}{6}}\right)^{1}\\= y^{ \frac{5}{6} . 1 }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
6. \(\left(y^{\frac{1}{5}}\right)^{\frac{-5}{3}}\\= y^{ \frac{1}{5} . (\frac{-5}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
7. \(\left(q^{\frac{1}{2}}\right)^{\frac{-4}{3}}\\= q^{ \frac{1}{2} . (\frac{-4}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
8. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-4}{5} . (\frac{-2}{3}) }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)
9. \(\left(y^{\frac{5}{4}}\right)^{\frac{-4}{5}}\\= y^{ \frac{5}{4} . (\frac{-4}{5}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
10. \(\left(y^{\frac{-5}{6}}\right)^{\frac{5}{4}}\\= y^{ \frac{-5}{6} . \frac{5}{4} }= y^{\frac{-25}{24}}\\=\frac{1}{\sqrt[24]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[24]{ y }}=\frac{1}{|y|.\sqrt[24]{ y }} \color{purple}{\frac{\sqrt[24]{ y^{23} }}{\sqrt[24]{ y^{23} }}} \\=\frac{\sqrt[24]{ y^{23} }}{|y^{2}|}\\---------------\)
11. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-5}{2}}\\= y^{ \frac{-1}{6} . (\frac{-5}{2}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
12. \(\left(y^{\frac{-5}{6}}\right)^{\frac{1}{6}}\\= y^{ \frac{-5}{6} . \frac{1}{6} }= y^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ y^{5} }}=\frac{1}{\sqrt[36]{ y^{5} }}. \color{purple}{\frac{\sqrt[36]{ y^{31} }}{\sqrt[36]{ y^{31} }}} \\=\frac{\sqrt[36]{ y^{31} }}{|y|}\\---------------\)