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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= x^{ \frac{1}{2} . (\frac{-1}{3}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
2. \(\left(x^{\frac{1}{5}}\right)^{\frac{5}{6}}\\= x^{ \frac{1}{5} . \frac{5}{6} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
3. \(\left(q^{\frac{1}{2}}\right)^{\frac{-1}{5}}\\= q^{ \frac{1}{2} . (\frac{-1}{5}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
4. \(\left(x^{\frac{-5}{2}}\right)^{\frac{1}{4}}\\= x^{ \frac{-5}{2} . \frac{1}{4} }= x^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ x^{5} }}=\frac{1}{\sqrt[8]{ x^{5} }}. \color{purple}{\frac{\sqrt[8]{ x^{3} }}{\sqrt[8]{ x^{3} }}} \\=\frac{\sqrt[8]{ x^{3} }}{|x|}\\---------------\)
5. \(\left(x^{1}\right)^{\frac{-5}{6}}\\= x^{ 1 . (\frac{-5}{6}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
6. \(\left(y^{\frac{3}{5}}\right)^{\frac{-2}{5}}\\= y^{ \frac{3}{5} . (\frac{-2}{5}) }= y^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ y^{6} }}=\frac{1}{\sqrt[25]{ y^{6} }}. \color{purple}{\frac{\sqrt[25]{ y^{19} }}{\sqrt[25]{ y^{19} }}} \\=\frac{\sqrt[25]{ y^{19} }}{y}\\---------------\)
7. \(\left(a^{\frac{-5}{4}}\right)^{-1}\\= a^{ \frac{-5}{4} . (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
8. \(\left(a^{\frac{1}{2}}\right)^{\frac{-5}{6}}\\= a^{ \frac{1}{2} . (\frac{-5}{6}) }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
9. \(\left(x^{\frac{1}{3}}\right)^{\frac{-3}{5}}\\= x^{ \frac{1}{3} . (\frac{-3}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
10. \(\left(y^{\frac{1}{4}}\right)^{\frac{-5}{3}}\\= y^{ \frac{1}{4} . (\frac{-5}{3}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
11. \(\left(q^{\frac{-5}{6}}\right)^{\frac{2}{5}}\\= q^{ \frac{-5}{6} . \frac{2}{5} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
12. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-1}{3} . (\frac{-1}{3}) }= x^{\frac{1}{9}}\\=\sqrt[9]{ x }\\---------------\)