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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{2} . \frac{1}{2} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
2. \(\left(y^{\frac{1}{3}}\right)^{1}\\= y^{ \frac{1}{3} . 1 }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
3. \(\left(x^{-1}\right)^{\frac{1}{4}}\\= x^{ -1 . \frac{1}{4} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
4. \(\left(q^{\frac{5}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{5}{2} . (\frac{-1}{2}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
5. \(\left(y^{\frac{5}{3}}\right)^{1}\\= y^{ \frac{5}{3} . 1 }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
6. \(\left(a^{\frac{2}{3}}\right)^{\frac{5}{2}}\\= a^{ \frac{2}{3} . \frac{5}{2} }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\left(q^{\frac{-3}{5}}\right)^{\frac{3}{4}}\\= q^{ \frac{-3}{5} . \frac{3}{4} }= q^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ q^{9} }}=\frac{1}{\sqrt[20]{ q^{9} }}. \color{purple}{\frac{\sqrt[20]{ q^{11} }}{\sqrt[20]{ q^{11} }}} \\=\frac{\sqrt[20]{ q^{11} }}{|q|}\\---------------\)
8. \(\left(q^{1}\right)^{\frac{5}{4}}\\= q^{ 1 . \frac{5}{4} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
9. \(\left(q^{\frac{4}{3}}\right)^{-2}\\= q^{ \frac{4}{3} . (-2) }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
10. \(\left(q^{\frac{5}{2}}\right)^{\frac{3}{4}}\\= q^{ \frac{5}{2} . \frac{3}{4} }= q^{\frac{15}{8}}\\=\sqrt[8]{ q^{15} }=|q|.\sqrt[8]{ q^{7} }\\---------------\)
11. \(\left(q^{-1}\right)^{2}\\= q^{ -1 . 2 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
12. \(\left(y^{-1}\right)^{\frac{1}{3}}\\= y^{ -1 . \frac{1}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)