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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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