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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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