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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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