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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{3}{5}}\right)^{\frac{-1}{3}}\\= a^{ \frac{3}{5} . (\frac{-1}{3}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
2. \(\left(x^{-1}\right)^{\frac{5}{4}}\\= x^{ -1 . \frac{5}{4} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
3. \(\left(y^{-1}\right)^{\frac{-1}{3}}\\= y^{ -1 . (\frac{-1}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
4. \(\left(q^{\frac{5}{3}}\right)^{-2}\\= q^{ \frac{5}{3} . (-2) }= q^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ q^{10} }}\\=\frac{1}{q^{3}.\sqrt[3]{ q }}=\frac{1}{q^{3}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{4}}\\---------------\)
5. \(\left(a^{\frac{-5}{6}}\right)^{\frac{3}{4}}\\= a^{ \frac{-5}{6} . \frac{3}{4} }= a^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ a^{5} }}=\frac{1}{\sqrt[8]{ a^{5} }}. \color{purple}{\frac{\sqrt[8]{ a^{3} }}{\sqrt[8]{ a^{3} }}} \\=\frac{\sqrt[8]{ a^{3} }}{|a|}\\---------------\)
6. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-5}{6} . (\frac{-3}{4}) }= y^{\frac{5}{8}}\\=\sqrt[8]{ y^{5} }\\---------------\)
7. \(\left(y^{\frac{-1}{4}}\right)^{\frac{1}{5}}\\= y^{ \frac{-1}{4} . \frac{1}{5} }= y^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ y }}=\frac{1}{\sqrt[20]{ y }}. \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y|}\\---------------\)
8. \(\left(x^{\frac{-5}{3}}\right)^{1}\\= x^{ \frac{-5}{3} . 1 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
9. \(\left(y^{\frac{3}{5}}\right)^{\frac{-1}{6}}\\= y^{ \frac{3}{5} . (\frac{-1}{6}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
10. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-1}{2} . (\frac{-5}{4}) }= q^{\frac{5}{8}}\\=\sqrt[8]{ q^{5} }\\---------------\)
11. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-1}{6}}\\= y^{ \frac{-1}{6} . (\frac{-1}{6}) }= y^{\frac{1}{36}}\\=\sqrt[36]{ y }\\---------------\)
12. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-1}{2} . (\frac{-2}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)