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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{-3}{4}}\\= q^{ 1 . (\frac{-3}{4}) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
2. \(\left(y^{2}\right)^{1}\\= y^{ 2 . 1 }= y^{2}\\\\---------------\)
3. \(\left(q^{\frac{2}{5}}\right)^{-1}\\= q^{ \frac{2}{5} . (-1) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
4. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-5}{6}}\\= a^{ \frac{-2}{5} . (\frac{-5}{6}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
5. \(\left(a^{1}\right)^{\frac{2}{5}}\\= a^{ 1 . \frac{2}{5} }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
6. \(\left(q^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{1}{2} . (\frac{-3}{4}) }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
7. \(\left(y^{\frac{1}{3}}\right)^{\frac{5}{6}}\\= y^{ \frac{1}{3} . \frac{5}{6} }= y^{\frac{5}{18}}\\=\sqrt[18]{ y^{5} }\\---------------\)
8. \(\left(y^{\frac{-5}{6}}\right)^{\frac{4}{3}}\\= y^{ \frac{-5}{6} . \frac{4}{3} }= y^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ y^{10} }}\\=\frac{1}{y.\sqrt[9]{ y }}=\frac{1}{y.\sqrt[9]{ y }} \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y^{2}}\\---------------\)
9. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-2}{3} . (\frac{-2}{3}) }= y^{\frac{4}{9}}\\=\sqrt[9]{ y^{4} }\\---------------\)
10. \(\left(y^{\frac{1}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{1}{3} . (\frac{-2}{3}) }= y^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ y^{2} }}=\frac{1}{\sqrt[9]{ y^{2} }}. \color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y}\\---------------\)
11. \(\left(q^{\frac{2}{5}}\right)^{\frac{1}{5}}\\= q^{ \frac{2}{5} . \frac{1}{5} }= q^{\frac{2}{25}}\\=\sqrt[25]{ q^{2} }\\---------------\)
12. \(\left(q^{-1}\right)^{\frac{2}{3}}\\= q^{ -1 . \frac{2}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)