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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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