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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{2}}\right)^{-1}\\= x^{ \frac{1}{2} . (-1) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
2. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{4}}\\= x^{ \frac{-1}{3} . \frac{1}{4} }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
3. \(\left(q^{\frac{-5}{4}}\right)^{\frac{1}{3}}\\= q^{ \frac{-5}{4} . \frac{1}{3} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
4. \(\left(y^{\frac{4}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{4}{3} . \frac{2}{3} }= y^{\frac{8}{9}}\\=\sqrt[9]{ y^{8} }\\---------------\)
5. \(\left(q^{\frac{4}{5}}\right)^{-1}\\= q^{ \frac{4}{5} . (-1) }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
6. \(\left(x^{\frac{1}{3}}\right)^{\frac{5}{6}}\\= x^{ \frac{1}{3} . \frac{5}{6} }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)
7. \(\left(a^{\frac{2}{5}}\right)^{1}\\= a^{ \frac{2}{5} . 1 }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
8. \(\left(q^{\frac{1}{2}}\right)^{\frac{3}{2}}\\= q^{ \frac{1}{2} . \frac{3}{2} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
9. \(\left(x^{\frac{3}{2}}\right)^{\frac{-5}{2}}\\= x^{ \frac{3}{2} . (\frac{-5}{2}) }= x^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ x^{15} }}\\=\frac{1}{|x^{3}|.\sqrt[4]{ x^{3} }}=\frac{1}{|x^{3}|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{4}|}\\---------------\)
10. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-2}{5}}\\= a^{ \frac{-1}{2} . (\frac{-2}{5}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
11. \(\left(y^{1}\right)^{\frac{2}{3}}\\= y^{ 1 . \frac{2}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
12. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-4}{5} . (\frac{-2}{3}) }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)