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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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