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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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