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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{4}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{4}{3} . \frac{1}{5} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
2. \(\left(x^{2}\right)^{1}\\= x^{ 2 . 1 }= x^{2}\\\\---------------\)
3. \(\left(q^{\frac{-1}{3}}\right)^{-2}\\= q^{ \frac{-1}{3} . (-2) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
4. \(\left(y^{\frac{-5}{4}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-5}{4} . (\frac{-5}{4}) }= y^{\frac{25}{16}}\\=\sqrt[16]{ y^{25} }=|y|.\sqrt[16]{ y^{9} }\\---------------\)
5. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-2}{3} . (\frac{-5}{3}) }= y^{\frac{10}{9}}\\=\sqrt[9]{ y^{10} }=y.\sqrt[9]{ y }\\---------------\)
6. \(\left(q^{\frac{2}{3}}\right)^{\frac{5}{3}}\\= q^{ \frac{2}{3} . \frac{5}{3} }= q^{\frac{10}{9}}\\=\sqrt[9]{ q^{10} }=q.\sqrt[9]{ q }\\---------------\)
7. \(\left(y^{1}\right)^{-1}\\= y^{ 1 . (-1) }= y^{-1}\\=\frac{1}{y}\\---------------\)
8. \(\left(x^{\frac{1}{4}}\right)^{-1}\\= x^{ \frac{1}{4} . (-1) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
9. \(\left(q^{\frac{5}{2}}\right)^{\frac{-2}{5}}\\= q^{ \frac{5}{2} . (\frac{-2}{5}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
10. \(\left(y^{\frac{-1}{2}}\right)^{-1}\\= y^{ \frac{-1}{2} . (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
11. \(\left(q^{\frac{-4}{5}}\right)^{\frac{5}{3}}\\= q^{ \frac{-4}{5} . \frac{5}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
12. \(\left(x^{\frac{-1}{6}}\right)^{\frac{2}{5}}\\= x^{ \frac{-1}{6} . \frac{2}{5} }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)