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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-2}{5} . (\frac{-3}{4}) }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
2. \(\left(q^{\frac{-5}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{-5}{3} . \frac{1}{5} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
3. \(\left(y^{\frac{-1}{2}}\right)^{\frac{3}{2}}\\= y^{ \frac{-1}{2} . \frac{3}{2} }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
4. \(\left(q^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{2} . (\frac{-1}{2}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
5. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-2}{3} . \frac{1}{2} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\left(a^{\frac{4}{5}}\right)^{\frac{-1}{6}}\\= a^{ \frac{4}{5} . (\frac{-1}{6}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
7. \(\left(y^{\frac{-5}{3}}\right)^{\frac{1}{6}}\\= y^{ \frac{-5}{3} . \frac{1}{6} }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
8. \(\left(a^{\frac{1}{2}}\right)^{-1}\\= a^{ \frac{1}{2} . (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
9. \(\left(q^{\frac{1}{5}}\right)^{\frac{-3}{2}}\\= q^{ \frac{1}{5} . (\frac{-3}{2}) }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
10. \(\left(q^{\frac{5}{6}}\right)^{-2}\\= q^{ \frac{5}{6} . (-2) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
11. \(\left(q^{\frac{-1}{3}}\right)^{-1}\\= q^{ \frac{-1}{3} . (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
12. \(\left(x^{\frac{-1}{2}}\right)^{\frac{3}{5}}\\= x^{ \frac{-1}{2} . \frac{3}{5} }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)