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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{5}{2}}\right)^{1}\\= q^{ \frac{5}{2} . 1 }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
2. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{5} . (\frac{-1}{2}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
3. \(\left(y^{\frac{1}{2}}\right)^{\frac{4}{3}}\\= y^{ \frac{1}{2} . \frac{4}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
4. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-1}{2} . (\frac{-5}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
5. \(\left(y^{\frac{2}{3}}\right)^{\frac{-5}{2}}\\= y^{ \frac{2}{3} . (\frac{-5}{2}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
6. \(\left(q^{\frac{-2}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{-2}{5} . \frac{1}{3} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
7. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-3}{5} . (\frac{-5}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
8. \(\left(y^{\frac{-5}{4}}\right)^{\frac{-1}{6}}\\= y^{ \frac{-5}{4} . (\frac{-1}{6}) }= y^{\frac{5}{24}}\\=\sqrt[24]{ y^{5} }\\---------------\)
9. \(\left(y^{\frac{1}{5}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{5} . \frac{1}{2} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
10. \(\left(x^{\frac{3}{5}}\right)^{\frac{5}{6}}\\= x^{ \frac{3}{5} . \frac{5}{6} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
11. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-2}{3} . (\frac{-3}{5}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
12. \(\left(q^{\frac{5}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{5}{2} . \frac{2}{3} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)