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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{5}}\right)^{-2}\\= q^{ \frac{-1}{5} . (-2) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
2. \(\left(x^{1}\right)^{\frac{1}{3}}\\= x^{ 1 . \frac{1}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
3. \(\left(x^{2}\right)^{\frac{-1}{5}}\\= x^{ 2 . (\frac{-1}{5}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
4. \(\left(x^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{2} . \frac{1}{2} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
5. \(\left(y^{\frac{5}{2}}\right)^{\frac{1}{5}}\\= y^{ \frac{5}{2} . \frac{1}{5} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
6. \(\left(y^{-1}\right)^{\frac{5}{4}}\\= y^{ -1 . \frac{5}{4} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
7. \(\left(x^{\frac{5}{6}}\right)^{\frac{-3}{5}}\\= x^{ \frac{5}{6} . (\frac{-3}{5}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{2} . (\frac{-2}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
9. \(\left(q^{\frac{1}{4}}\right)^{\frac{-3}{5}}\\= q^{ \frac{1}{4} . (\frac{-3}{5}) }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
10. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-1}{2} . (\frac{-1}{3}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
11. \(\left(a^{\frac{2}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{2}{5} . (\frac{-2}{3}) }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
12. \(\left(y^{\frac{1}{5}}\right)^{\frac{1}{6}}\\= y^{ \frac{1}{5} . \frac{1}{6} }= y^{\frac{1}{30}}\\=\sqrt[30]{ y }\\---------------\)