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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-1}{2} . (\frac{-3}{4}) }= y^{\frac{3}{8}}\\=\sqrt[8]{ y^{3} }\\---------------\)
2. \(\left(y^{\frac{-1}{3}}\right)^{\frac{3}{5}}\\= y^{ \frac{-1}{3} . \frac{3}{5} }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
3. \(\left(a^{\frac{1}{4}}\right)^{\frac{1}{5}}\\= a^{ \frac{1}{4} . \frac{1}{5} }= a^{\frac{1}{20}}\\=\sqrt[20]{ a }\\---------------\)
4. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-3}{4} . (\frac{-4}{5}) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
5. \(\left(a^{\frac{-1}{3}}\right)^{\frac{3}{2}}\\= a^{ \frac{-1}{3} . \frac{3}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
6. \(\left(a^{1}\right)^{\frac{3}{5}}\\= a^{ 1 . \frac{3}{5} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
7. \(\left(y^{\frac{-2}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{-2}{3} . \frac{2}{3} }= y^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ y^{4} }}=\frac{1}{\sqrt[9]{ y^{4} }}. \color{purple}{\frac{\sqrt[9]{ y^{5} }}{\sqrt[9]{ y^{5} }}} \\=\frac{\sqrt[9]{ y^{5} }}{y}\\---------------\)
8. \(\left(a^{\frac{-4}{5}}\right)^{\frac{4}{3}}\\= a^{ \frac{-4}{5} . \frac{4}{3} }= a^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ a^{16} }}\\=\frac{1}{a.\sqrt[15]{ a }}=\frac{1}{a.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{2}}\\---------------\)
9. \(\left(x^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{2} . \frac{1}{2} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
10. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-2}{3} . (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
11. \(\left(y^{\frac{1}{2}}\right)^{\frac{5}{6}}\\= y^{ \frac{1}{2} . \frac{5}{6} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
12. \(\left(q^{\frac{1}{2}}\right)^{1}\\= q^{ \frac{1}{2} . 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)