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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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