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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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