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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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