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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{4}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{4} . (\frac{-1}{2}) }= x^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ x }}=\frac{1}{\sqrt[8]{ x }}. \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x|}\\---------------\)
2. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-2}{5} . (\frac{-3}{5}) }= y^{\frac{6}{25}}\\=\sqrt[25]{ y^{6} }\\---------------\)
3. \(\left(a^{\frac{1}{6}}\right)^{\frac{2}{3}}\\= a^{ \frac{1}{6} . \frac{2}{3} }= a^{\frac{1}{9}}\\=\sqrt[9]{ a }\\---------------\)
4. \(\left(a^{\frac{-1}{4}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-1}{4} . (\frac{-2}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
5. \(\left(y^{\frac{4}{3}}\right)^{\frac{4}{5}}\\= y^{ \frac{4}{3} . \frac{4}{5} }= y^{\frac{16}{15}}\\=\sqrt[15]{ y^{16} }=y.\sqrt[15]{ y }\\---------------\)
6. \(\left(a^{\frac{-2}{5}}\right)^{\frac{1}{2}}\\= a^{ \frac{-2}{5} . \frac{1}{2} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
7. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-5}{4} . (\frac{-1}{2}) }= q^{\frac{5}{8}}\\=\sqrt[8]{ q^{5} }\\---------------\)
8. \(\left(x^{\frac{3}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{3}{4} . \frac{1}{2} }= x^{\frac{3}{8}}\\=\sqrt[8]{ x^{3} }\\---------------\)
9. \(\left(q^{\frac{-5}{4}}\right)^{\frac{3}{5}}\\= q^{ \frac{-5}{4} . \frac{3}{5} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
10. \(\left(q^{2}\right)^{\frac{5}{6}}\\= q^{ 2 . \frac{5}{6} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
11. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-4}{3} . (\frac{-1}{2}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
12. \(\left(x^{-2}\right)^{\frac{1}{5}}\\= x^{ -2 . \frac{1}{5} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)