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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{4} . (\frac{-1}{2}) }= y^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ y }}=\frac{1}{\sqrt[8]{ y }}. \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y|}\\---------------\)
2. \(\left(x^{\frac{3}{2}}\right)^{\frac{3}{5}}\\= x^{ \frac{3}{2} . \frac{3}{5} }= x^{\frac{9}{10}}\\=\sqrt[10]{ x^{9} }\\---------------\)
3. \(\left(y^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{2} . \frac{2}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
4. \(\left(a^{-1}\right)^{\frac{-1}{3}}\\= a^{ -1 . (\frac{-1}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
5. \(\left(x^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{2} . (\frac{-1}{2}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
6. \(\left(x^{\frac{3}{2}}\right)^{\frac{4}{5}}\\= x^{ \frac{3}{2} . \frac{4}{5} }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
7. \(\left(a^{-2}\right)^{\frac{-4}{5}}\\= a^{ -2 . (\frac{-4}{5}) }= a^{\frac{8}{5}}\\=\sqrt[5]{ a^{8} }=a.\sqrt[5]{ a^{3} }\\---------------\)
8. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-4}{3}}\\= x^{ \frac{-4}{5} . (\frac{-4}{3}) }= x^{\frac{16}{15}}\\=\sqrt[15]{ x^{16} }=x.\sqrt[15]{ x }\\---------------\)
9. \(\left(q^{\frac{1}{3}}\right)^{1}\\= q^{ \frac{1}{3} . 1 }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\left(a^{\frac{-1}{6}}\right)^{\frac{3}{5}}\\= a^{ \frac{-1}{6} . \frac{3}{5} }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
11. \(\left(a^{\frac{-1}{3}}\right)^{-1}\\= a^{ \frac{-1}{3} . (-1) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
12. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{3} . \frac{1}{2} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)