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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{4}{3}}\right)^{\frac{-5}{6}}\\= q^{ \frac{4}{3} . (\frac{-5}{6}) }= q^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ q^{10} }}\\=\frac{1}{q.\sqrt[9]{ q }}=\frac{1}{q.\sqrt[9]{ q }} \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q^{2}}\\---------------\)
2. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-1}{3} . (\frac{-1}{4}) }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
3. \(\left(q^{\frac{2}{3}}\right)^{\frac{3}{2}}\\= q^{ \frac{2}{3} . \frac{3}{2} }= q^{1}\\\\---------------\)
4. \(\left(a^{\frac{1}{4}}\right)^{\frac{-5}{6}}\\= a^{ \frac{1}{4} . (\frac{-5}{6}) }= a^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ a^{5} }}=\frac{1}{\sqrt[24]{ a^{5} }}. \color{purple}{\frac{\sqrt[24]{ a^{19} }}{\sqrt[24]{ a^{19} }}} \\=\frac{\sqrt[24]{ a^{19} }}{|a|}\\---------------\)
5. \(\left(q^{\frac{-1}{4}}\right)^{-1}\\= q^{ \frac{-1}{4} . (-1) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
6. \(\left(q^{\frac{3}{2}}\right)^{1}\\= q^{ \frac{3}{2} . 1 }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
7. \(\left(x^{\frac{-2}{3}}\right)^{\frac{3}{4}}\\= x^{ \frac{-2}{3} . \frac{3}{4} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\left(x^{\frac{-1}{2}}\right)^{-1}\\= x^{ \frac{-1}{2} . (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
9. \(\left(q^{-1}\right)^{\frac{3}{5}}\\= q^{ -1 . \frac{3}{5} }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
10. \(\left(q^{\frac{-5}{2}}\right)^{\frac{3}{2}}\\= q^{ \frac{-5}{2} . \frac{3}{2} }= q^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ q^{15} }}\\=\frac{1}{|q^{3}|.\sqrt[4]{ q^{3} }}=\frac{1}{|q^{3}|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{4}|}\\---------------\)
11. \(\left(x^{1}\right)^{-1}\\= x^{ 1 . (-1) }= x^{-1}\\=\frac{1}{x}\\---------------\)
12. \(\left(y^{-2}\right)^{\frac{1}{4}}\\= y^{ -2 . \frac{1}{4} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)