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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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