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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{2}}\right)^{1}\\= y^{ \frac{1}{2} . 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
2. \(\left(q^{\frac{1}{3}}\right)^{\frac{3}{5}}\\= q^{ \frac{1}{3} . \frac{3}{5} }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
3. \(\left(a^{2}\right)^{\frac{1}{2}}\\= a^{ 2 . \frac{1}{2} }= a^{1}\\\\---------------\)
4. \(\left(q^{\frac{3}{4}}\right)^{-1}\\= q^{ \frac{3}{4} . (-1) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
5. \(\left(q^{\frac{1}{2}}\right)^{\frac{5}{4}}\\= q^{ \frac{1}{2} . \frac{5}{4} }= q^{\frac{5}{8}}\\=\sqrt[8]{ q^{5} }\\---------------\)
6. \(\left(x^{\frac{-1}{5}}\right)^{\frac{1}{5}}\\= x^{ \frac{-1}{5} . \frac{1}{5} }= x^{\frac{-1}{25}}\\=\frac{1}{\sqrt[25]{ x }}=\frac{1}{\sqrt[25]{ x }}. \color{purple}{\frac{\sqrt[25]{ x^{24} }}{\sqrt[25]{ x^{24} }}} \\=\frac{\sqrt[25]{ x^{24} }}{x}\\---------------\)
7. \(\left(x^{-1}\right)^{\frac{5}{3}}\\= x^{ -1 . \frac{5}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
8. \(\left(y^{\frac{1}{2}}\right)^{\frac{4}{5}}\\= y^{ \frac{1}{2} . \frac{4}{5} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
9. \(\left(x^{\frac{-1}{6}}\right)^{\frac{3}{5}}\\= x^{ \frac{-1}{6} . \frac{3}{5} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
10. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
11. \(\left(a^{\frac{1}{2}}\right)^{\frac{-5}{4}}\\= a^{ \frac{1}{2} . (\frac{-5}{4}) }= a^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ a^{5} }}=\frac{1}{\sqrt[8]{ a^{5} }}. \color{purple}{\frac{\sqrt[8]{ a^{3} }}{\sqrt[8]{ a^{3} }}} \\=\frac{\sqrt[8]{ a^{3} }}{|a|}\\---------------\)
12. \(\left(q^{\frac{1}{3}}\right)^{\frac{5}{6}}\\= q^{ \frac{1}{3} . \frac{5}{6} }= q^{\frac{5}{18}}\\=\sqrt[18]{ q^{5} }\\---------------\)