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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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