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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-3}{2}}\right)^{1}\\= y^{ \frac{-3}{2} . 1 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
2. \(\left(a^{\frac{1}{3}}\right)^{1}\\= a^{ \frac{1}{3} . 1 }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
3. \(\left(y^{\frac{2}{5}}\right)^{1}\\= y^{ \frac{2}{5} . 1 }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
4. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-5}{2}}\\= y^{ \frac{-1}{3} . (\frac{-5}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
5. \(\left(x^{1}\right)^{\frac{5}{6}}\\= x^{ 1 . \frac{5}{6} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
6. \(\left(q^{\frac{2}{5}}\right)^{\frac{1}{5}}\\= q^{ \frac{2}{5} . \frac{1}{5} }= q^{\frac{2}{25}}\\=\sqrt[25]{ q^{2} }\\---------------\)
7. \(\left(q^{-2}\right)^{\frac{3}{4}}\\= q^{ -2 . \frac{3}{4} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
8. \(\left(q^{\frac{2}{3}}\right)^{1}\\= q^{ \frac{2}{3} . 1 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
9. \(\left(x^{\frac{-3}{2}}\right)^{\frac{1}{6}}\\= x^{ \frac{-3}{2} . \frac{1}{6} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
10. \(\left(a^{\frac{1}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{1}{5} . (\frac{-2}{3}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
11. \(\left(y^{\frac{1}{2}}\right)^{\frac{-5}{6}}\\= y^{ \frac{1}{2} . (\frac{-5}{6}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
12. \(\left(a^{\frac{4}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{4}{3} . (\frac{-1}{3}) }= a^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ a^{4} }}=\frac{1}{\sqrt[9]{ a^{4} }}. \color{purple}{\frac{\sqrt[9]{ a^{5} }}{\sqrt[9]{ a^{5} }}} \\=\frac{\sqrt[9]{ a^{5} }}{a}\\---------------\)