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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{1}\right)^{\frac{3}{5}}\\= y^{ 1 . \frac{3}{5} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
2. \(\left(q^{1}\right)^{\frac{5}{6}}\\= q^{ 1 . \frac{5}{6} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
3. \(\left(q^{-2}\right)^{\frac{-4}{3}}\\= q^{ -2 . (\frac{-4}{3}) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
4. \(\left(q^{\frac{-2}{3}}\right)^{\frac{5}{6}}\\= q^{ \frac{-2}{3} . \frac{5}{6} }= q^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ q^{5} }}=\frac{1}{\sqrt[9]{ q^{5} }}. \color{purple}{\frac{\sqrt[9]{ q^{4} }}{\sqrt[9]{ q^{4} }}} \\=\frac{\sqrt[9]{ q^{4} }}{q}\\---------------\)
5. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-5}{3} . (\frac{-1}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
6. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-2}{3} . (\frac{-1}{2}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
7. \(\left(y^{\frac{1}{3}}\right)^{\frac{-5}{3}}\\= y^{ \frac{1}{3} . (\frac{-5}{3}) }= y^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ y^{5} }}=\frac{1}{\sqrt[9]{ y^{5} }}. \color{purple}{\frac{\sqrt[9]{ y^{4} }}{\sqrt[9]{ y^{4} }}} \\=\frac{\sqrt[9]{ y^{4} }}{y}\\---------------\)
8. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{4}}\\= q^{ \frac{1}{2} . (\frac{-5}{4}) }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
9. \(\left(y^{1}\right)^{\frac{-5}{4}}\\= y^{ 1 . (\frac{-5}{4}) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
10. \(\left(q^{\frac{1}{3}}\right)^{-1}\\= q^{ \frac{1}{3} . (-1) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
11. \(\left(y^{\frac{-4}{5}}\right)^{\frac{4}{5}}\\= y^{ \frac{-4}{5} . \frac{4}{5} }= y^{\frac{-16}{25}}\\=\frac{1}{\sqrt[25]{ y^{16} }}=\frac{1}{\sqrt[25]{ y^{16} }}. \color{purple}{\frac{\sqrt[25]{ y^{9} }}{\sqrt[25]{ y^{9} }}} \\=\frac{\sqrt[25]{ y^{9} }}{y}\\---------------\)
12. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{1}{3} . \frac{1}{5} }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)