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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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