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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-5}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-5}{4} . (\frac{-1}{2}) }= y^{\frac{5}{8}}\\=\sqrt[8]{ y^{5} }\\---------------\)
2. \(\left(q^{-1}\right)^{1}\\= q^{ -1 . 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)
3. \(\left(q^{-1}\right)^{\frac{5}{4}}\\= q^{ -1 . \frac{5}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
4. \(\left(a^{\frac{-4}{3}}\right)^{\frac{5}{6}}\\= a^{ \frac{-4}{3} . \frac{5}{6} }= a^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ a^{10} }}\\=\frac{1}{a.\sqrt[9]{ a }}=\frac{1}{a.\sqrt[9]{ a }} \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a^{2}}\\---------------\)
5. \(\left(a^{1}\right)^{\frac{-4}{5}}\\= a^{ 1 . (\frac{-4}{5}) }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
6. \(\left(q^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{1}{2} . (\frac{-2}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{4}}\\= a^{ \frac{1}{3} . \frac{1}{4} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
8. \(\left(y^{\frac{2}{3}}\right)^{\frac{2}{5}}\\= y^{ \frac{2}{3} . \frac{2}{5} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
9. \(\left(y^{\frac{-1}{6}}\right)^{1}\\= y^{ \frac{-1}{6} . 1 }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
10. \(\left(q^{\frac{-2}{3}}\right)^{\frac{4}{3}}\\= q^{ \frac{-2}{3} . \frac{4}{3} }= q^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ q^{8} }}=\frac{1}{\sqrt[9]{ q^{8} }}. \color{purple}{\frac{\sqrt[9]{ q }}{\sqrt[9]{ q }}} \\=\frac{\sqrt[9]{ q }}{q}\\---------------\)
11. \(\left(a^{\frac{4}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{4}{5} . (\frac{-3}{5}) }= a^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ a^{12} }}=\frac{1}{\sqrt[25]{ a^{12} }}. \color{purple}{\frac{\sqrt[25]{ a^{13} }}{\sqrt[25]{ a^{13} }}} \\=\frac{\sqrt[25]{ a^{13} }}{a}\\---------------\)
12. \(\left(y^{\frac{2}{3}}\right)^{\frac{5}{6}}\\= y^{ \frac{2}{3} . \frac{5}{6} }= y^{\frac{5}{9}}\\=\sqrt[9]{ y^{5} }\\---------------\)