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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{5}{2} . (\frac{-2}{3}) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
2. \(\left(q^{2}\right)^{\frac{1}{6}}\\= q^{ 2 . \frac{1}{6} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
3. \(\left(a^{1}\right)^{\frac{-1}{2}}\\= a^{ 1 . (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
4. \(\left(y^{-1}\right)^{\frac{-1}{3}}\\= y^{ -1 . (\frac{-1}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
5. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-3}{2}}\\= y^{ \frac{-5}{3} . (\frac{-3}{2}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
6. \(\left(a^{1}\right)^{\frac{4}{3}}\\= a^{ 1 . \frac{4}{3} }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
7. \(\left(y^{1}\right)^{\frac{-1}{4}}\\= y^{ 1 . (\frac{-1}{4}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
8. \(\left(q^{\frac{2}{5}}\right)^{1}\\= q^{ \frac{2}{5} . 1 }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
9. \(\left(x^{\frac{-1}{4}}\right)^{\frac{1}{3}}\\= x^{ \frac{-1}{4} . \frac{1}{3} }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
10. \(\left(q^{\frac{5}{6}}\right)^{\frac{5}{2}}\\= q^{ \frac{5}{6} . \frac{5}{2} }= q^{\frac{25}{12}}\\=\sqrt[12]{ q^{25} }=|q^{2}|.\sqrt[12]{ q }\\---------------\)
11. \(\left(y^{\frac{4}{5}}\right)^{\frac{-4}{5}}\\= y^{ \frac{4}{5} . (\frac{-4}{5}) }= y^{\frac{-16}{25}}\\=\frac{1}{\sqrt[25]{ y^{16} }}=\frac{1}{\sqrt[25]{ y^{16} }}. \color{purple}{\frac{\sqrt[25]{ y^{9} }}{\sqrt[25]{ y^{9} }}} \\=\frac{\sqrt[25]{ y^{9} }}{y}\\---------------\)
12. \(\left(x^{\frac{5}{4}}\right)^{\frac{-1}{6}}\\= x^{ \frac{5}{4} . (\frac{-1}{6}) }= x^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ x^{5} }}=\frac{1}{\sqrt[24]{ x^{5} }}. \color{purple}{\frac{\sqrt[24]{ x^{19} }}{\sqrt[24]{ x^{19} }}} \\=\frac{\sqrt[24]{ x^{19} }}{|x|}\\---------------\)