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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{2} . \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
2. \(\left(x^{1}\right)^{\frac{3}{5}}\\= x^{ 1 . \frac{3}{5} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
3. \(\left(x^{\frac{2}{3}}\right)^{\frac{-1}{4}}\\= x^{ \frac{2}{3} . (\frac{-1}{4}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
4. \(\left(q^{\frac{1}{3}}\right)^{\frac{-5}{4}}\\= q^{ \frac{1}{3} . (\frac{-5}{4}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
5. \(\left(q^{\frac{-5}{6}}\right)^{\frac{5}{3}}\\= q^{ \frac{-5}{6} . \frac{5}{3} }= q^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ q^{25} }}\\=\frac{1}{|q|.\sqrt[18]{ q^{7} }}=\frac{1}{|q|.\sqrt[18]{ q^{7} }} \color{purple}{\frac{\sqrt[18]{ q^{11} }}{\sqrt[18]{ q^{11} }}} \\=\frac{\sqrt[18]{ q^{11} }}{|q^{2}|}\\---------------\)
6. \(\left(y^{\frac{1}{4}}\right)^{-2}\\= y^{ \frac{1}{4} . (-2) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
7. \(\left(a^{\frac{-1}{6}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-1}{6} . (\frac{-1}{3}) }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
8. \(\left(x^{\frac{-1}{4}}\right)^{\frac{4}{5}}\\= x^{ \frac{-1}{4} . \frac{4}{5} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
9. \(\left(y^{\frac{1}{4}}\right)^{\frac{-5}{4}}\\= y^{ \frac{1}{4} . (\frac{-5}{4}) }= y^{\frac{-5}{16}}\\=\frac{1}{\sqrt[16]{ y^{5} }}=\frac{1}{\sqrt[16]{ y^{5} }}. \color{purple}{\frac{\sqrt[16]{ y^{11} }}{\sqrt[16]{ y^{11} }}} \\=\frac{\sqrt[16]{ y^{11} }}{|y|}\\---------------\)
10. \(\left(x^{\frac{-4}{3}}\right)^{\frac{5}{4}}\\= x^{ \frac{-4}{3} . \frac{5}{4} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
11. \(\left(a^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= a^{ \frac{1}{2} . (\frac{-3}{4}) }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)
12. \(\left(a^{\frac{-2}{5}}\right)^{1}\\= a^{ \frac{-2}{5} . 1 }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)