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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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