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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{4}}\right)^{-1}\\= q^{ \frac{-5}{4} . (-1) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
2. \(\left(q^{2}\right)^{\frac{-2}{3}}\\= q^{ 2 . (\frac{-2}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
3. \(\left(y^{\frac{3}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{3}{2} . (\frac{-1}{3}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
4. \(\left(y^{1}\right)^{\frac{4}{3}}\\= y^{ 1 . \frac{4}{3} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
5. \(\left(y^{\frac{-4}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{-4}{3} . \frac{1}{2} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
6. \(\left(a^{\frac{-1}{4}}\right)^{1}\\= a^{ \frac{-1}{4} . 1 }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
7. \(\left(x^{\frac{3}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{3}{5} . \frac{1}{2} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
8. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-1}{2} . (\frac{-3}{4}) }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)
9. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-5}{3} . (\frac{-3}{2}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{2} . (\frac{-1}{2}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
11. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{-1}{3} . \frac{1}{5} }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
12. \(\left(a^{-1}\right)^{-1}\\= a^{ -1 . (-1) }= a^{1}\\\\---------------\)