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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-5}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-5}{2} . \frac{1}{2} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
2. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
3. \(\left(x^{\frac{3}{5}}\right)^{\frac{-1}{4}}\\= x^{ \frac{3}{5} . (\frac{-1}{4}) }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)
4. \(\left(x^{\frac{5}{6}}\right)^{1}\\= x^{ \frac{5}{6} . 1 }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
5. \(\left(a^{\frac{-5}{6}}\right)^{\frac{3}{4}}\\= a^{ \frac{-5}{6} . \frac{3}{4} }= a^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ a^{5} }}=\frac{1}{\sqrt[8]{ a^{5} }}. \color{purple}{\frac{\sqrt[8]{ a^{3} }}{\sqrt[8]{ a^{3} }}} \\=\frac{\sqrt[8]{ a^{3} }}{|a|}\\---------------\)
6. \(\left(q^{\frac{4}{5}}\right)^{\frac{-5}{6}}\\= q^{ \frac{4}{5} . (\frac{-5}{6}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
7. \(\left(q^{\frac{4}{3}}\right)^{\frac{-2}{3}}\\= q^{ \frac{4}{3} . (\frac{-2}{3}) }= q^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ q^{8} }}=\frac{1}{\sqrt[9]{ q^{8} }}. \color{purple}{\frac{\sqrt[9]{ q }}{\sqrt[9]{ q }}} \\=\frac{\sqrt[9]{ q }}{q}\\---------------\)
8. \(\left(q^{\frac{-3}{5}}\right)^{\frac{1}{4}}\\= q^{ \frac{-3}{5} . \frac{1}{4} }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
9. \(\left(a^{\frac{5}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{5}{2} . (\frac{-1}{3}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
10. \(\left(a^{\frac{-1}{2}}\right)^{\frac{3}{2}}\\= a^{ \frac{-1}{2} . \frac{3}{2} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
11. \(\left(q^{\frac{1}{2}}\right)^{\frac{-1}{5}}\\= q^{ \frac{1}{2} . (\frac{-1}{5}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
12. \(\left(a^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{2} . \frac{1}{2} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)