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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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