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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{5}{4} . \frac{1}{2} }= a^{\frac{5}{8}}\\=\sqrt[8]{ a^{5} }\\---------------\)
2. \(\left(a^{1}\right)^{\frac{1}{2}}\\= a^{ 1 . \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
3. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{3} . (\frac{-2}{5}) }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
4. \(\left(y^{\frac{1}{2}}\right)^{1}\\= y^{ \frac{1}{2} . 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{3}{4}}\\= q^{ \frac{-1}{2} . \frac{3}{4} }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
6. \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{3}}\\= a^{ \frac{1}{6} . \frac{1}{3} }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
7. \(\left(y^{\frac{4}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{4}{3} . \frac{1}{2} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
8. \(\left(y^{\frac{-4}{3}}\right)^{\frac{4}{3}}\\= y^{ \frac{-4}{3} . \frac{4}{3} }= y^{\frac{-16}{9}}\\=\frac{1}{\sqrt[9]{ y^{16} }}\\=\frac{1}{y.\sqrt[9]{ y^{7} }}=\frac{1}{y.\sqrt[9]{ y^{7} }} \color{purple}{\frac{\sqrt[9]{ y^{2} }}{\sqrt[9]{ y^{2} }}} \\=\frac{\sqrt[9]{ y^{2} }}{y^{2}}\\---------------\)
9. \(\left(x^{\frac{-1}{6}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-1}{6} . (\frac{-4}{5}) }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)
10. \(\left(a^{\frac{1}{2}}\right)^{\frac{-3}{2}}\\= a^{ \frac{1}{2} . (\frac{-3}{2}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
11. \(\left(x^{\frac{-1}{2}}\right)^{1}\\= x^{ \frac{-1}{2} . 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
12. \(\left(q^{\frac{-3}{5}}\right)^{\frac{4}{5}}\\= q^{ \frac{-3}{5} . \frac{4}{5} }= q^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ q^{12} }}=\frac{1}{\sqrt[25]{ q^{12} }}. \color{purple}{\frac{\sqrt[25]{ q^{13} }}{\sqrt[25]{ q^{13} }}} \\=\frac{\sqrt[25]{ q^{13} }}{q}\\---------------\)