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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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