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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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