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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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