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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{3}{2}}\right)^{-1}\\= q^{ \frac{3}{2} . (-1) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
2. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-3}{4}}\\= x^{ \frac{-1}{2} . (\frac{-3}{4}) }= x^{\frac{3}{8}}\\=\sqrt[8]{ x^{3} }\\---------------\)
3. \(\left(q^{\frac{1}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{1}{3} . \frac{1}{5} }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
4. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-4}{3}}\\= y^{ \frac{-2}{5} . (\frac{-4}{3}) }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)
5. \(\left(y^{\frac{-5}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{-5}{3} . \frac{1}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
6. \(\left(q^{\frac{2}{3}}\right)^{-1}\\= q^{ \frac{2}{3} . (-1) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
7. \(\left(x^{\frac{5}{3}}\right)^{1}\\= x^{ \frac{5}{3} . 1 }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
8. \(\left(q^{\frac{-1}{3}}\right)^{-1}\\= q^{ \frac{-1}{3} . (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
9. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-5}{6}}\\= q^{ \frac{-1}{6} . (\frac{-5}{6}) }= q^{\frac{5}{36}}\\=\sqrt[36]{ q^{5} }\\---------------\)
10. \(\left(y^{\frac{-3}{4}}\right)^{\frac{5}{6}}\\= y^{ \frac{-3}{4} . \frac{5}{6} }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}. \color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)
11. \(\left(x^{\frac{-5}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{-5}{3} . \frac{2}{3} }= x^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ x^{10} }}\\=\frac{1}{x.\sqrt[9]{ x }}=\frac{1}{x.\sqrt[9]{ x }} \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x^{2}}\\---------------\)
12. \(\left(a^{\frac{-1}{2}}\right)^{\frac{4}{5}}\\= a^{ \frac{-1}{2} . \frac{4}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)