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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-5}{3} . (\frac{-1}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
2. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-1}{3} . (\frac{-4}{5}) }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
3. \(\left(y^{\frac{1}{2}}\right)^{-1}\\= y^{ \frac{1}{2} . (-1) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
4. \(\left(q^{\frac{-1}{6}}\right)^{\frac{5}{6}}\\= q^{ \frac{-1}{6} . \frac{5}{6} }= q^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ q^{5} }}=\frac{1}{\sqrt[36]{ q^{5} }}. \color{purple}{\frac{\sqrt[36]{ q^{31} }}{\sqrt[36]{ q^{31} }}} \\=\frac{\sqrt[36]{ q^{31} }}{|q|}\\---------------\)
5. \(\left(x^{2}\right)^{\frac{-3}{5}}\\= x^{ 2 . (\frac{-3}{5}) }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
6. \(\left(y^{\frac{3}{4}}\right)^{\frac{-3}{5}}\\= y^{ \frac{3}{4} . (\frac{-3}{5}) }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
7. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-4}{3}}\\= q^{ \frac{-1}{3} . (\frac{-4}{3}) }= q^{\frac{4}{9}}\\=\sqrt[9]{ q^{4} }\\---------------\)
8. \(\left(y^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{2} . \frac{2}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
9. \(\left(y^{\frac{-3}{2}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-3}{2} . (\frac{-3}{4}) }= y^{\frac{9}{8}}\\=\sqrt[8]{ y^{9} }=|y|.\sqrt[8]{ y }\\---------------\)
10. \(\left(a^{\frac{1}{3}}\right)^{\frac{5}{4}}\\= a^{ \frac{1}{3} . \frac{5}{4} }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
11. \(\left(a^{\frac{2}{5}}\right)^{\frac{-4}{5}}\\= a^{ \frac{2}{5} . (\frac{-4}{5}) }= a^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ a^{8} }}=\frac{1}{\sqrt[25]{ a^{8} }}. \color{purple}{\frac{\sqrt[25]{ a^{17} }}{\sqrt[25]{ a^{17} }}} \\=\frac{\sqrt[25]{ a^{17} }}{a}\\---------------\)
12. \(\left(y^{\frac{-1}{2}}\right)^{\frac{5}{4}}\\= y^{ \frac{-1}{2} . \frac{5}{4} }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}. \color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)