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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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