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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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