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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{-1}\right)^{\frac{-1}{6}}\\= y^{ -1 . (\frac{-1}{6}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
2. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)
3. \(\left(q^{\frac{4}{3}}\right)^{\frac{-3}{4}}\\= q^{ \frac{4}{3} . (\frac{-3}{4}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
4. \(\left(y^{-1}\right)^{\frac{-4}{3}}\\= y^{ -1 . (\frac{-4}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
5. \(\left(q^{\frac{2}{3}}\right)^{\frac{-5}{4}}\\= q^{ \frac{2}{3} . (\frac{-5}{4}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
6. \(\left(q^{\frac{-1}{3}}\right)^{\frac{5}{6}}\\= q^{ \frac{-1}{3} . \frac{5}{6} }= q^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ q^{5} }}=\frac{1}{\sqrt[18]{ q^{5} }}. \color{purple}{\frac{\sqrt[18]{ q^{13} }}{\sqrt[18]{ q^{13} }}} \\=\frac{\sqrt[18]{ q^{13} }}{|q|}\\---------------\)
7. \(\left(q^{\frac{-3}{4}}\right)^{-1}\\= q^{ \frac{-3}{4} . (-1) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
8. \(\left(a^{1}\right)^{\frac{-5}{3}}\\= a^{ 1 . (\frac{-5}{3}) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
9. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-2}{3} . (\frac{-3}{2}) }= x^{1}\\\\---------------\)
10. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-3}{4} . (\frac{-1}{2}) }= y^{\frac{3}{8}}\\=\sqrt[8]{ y^{3} }\\---------------\)
11. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{4}}\\= y^{ \frac{2}{3} . (\frac{-1}{4}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
12. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-2}{3} . (\frac{-1}{3}) }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)