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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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