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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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