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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{3}}\right)^{\frac{4}{5}}\\= y^{ \frac{-1}{3} . \frac{4}{5} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
2. \(\left(y^{\frac{-5}{3}}\right)^{\frac{5}{3}}\\= y^{ \frac{-5}{3} . \frac{5}{3} }= y^{\frac{-25}{9}}\\=\frac{1}{\sqrt[9]{ y^{25} }}\\=\frac{1}{y^{2}.\sqrt[9]{ y^{7} }}=\frac{1}{y^{2}.\sqrt[9]{ y^{7} }} \color{purple}{\frac{\sqrt[9]{ y^{2} }}{\sqrt[9]{ y^{2} }}} \\=\frac{\sqrt[9]{ y^{2} }}{y^{3}}\\---------------\)
3. \(\left(q^{\frac{-4}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{-4}{3} . \frac{1}{4} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
4. \(\left(a^{-1}\right)^{\frac{1}{2}}\\= a^{ -1 . \frac{1}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
5. \(\left(q^{\frac{-2}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{-2}{3} . \frac{1}{4} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
6. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
7. \(\left(x^{\frac{4}{3}}\right)^{\frac{-3}{2}}\\= x^{ \frac{4}{3} . (\frac{-3}{2}) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
8. \(\left(q^{\frac{3}{4}}\right)^{\frac{-1}{5}}\\= q^{ \frac{3}{4} . (\frac{-1}{5}) }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
9. \(\left(x^{\frac{1}{4}}\right)^{\frac{-5}{3}}\\= x^{ \frac{1}{4} . (\frac{-5}{3}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
10. \(\left(a^{\frac{-4}{5}}\right)^{-1}\\= a^{ \frac{-4}{5} . (-1) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
11. \(\left(x^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{3} . \frac{1}{2} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
12. \(\left(y^{\frac{-2}{3}}\right)^{-1}\\= y^{ \frac{-2}{3} . (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)