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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{3}{2}}\right)^{\frac{-5}{3}}\\= y^{ \frac{3}{2} . (\frac{-5}{3}) }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
2. \(\left(q^{\frac{-1}{5}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-1}{5} . (\frac{-5}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
3. \(\left(a^{-1}\right)^{\frac{-4}{5}}\\= a^{ -1 . (\frac{-4}{5}) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
4. \(\left(y^{\frac{3}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{3}{4} . (\frac{-1}{2}) }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)
5. \(\left(a^{\frac{1}{5}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{5} . \frac{1}{2} }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
6. \(\left(a^{\frac{5}{2}}\right)^{\frac{-1}{6}}\\= a^{ \frac{5}{2} . (\frac{-1}{6}) }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
7. \(\left(y^{\frac{1}{4}}\right)^{\frac{-1}{3}}\\= y^{ \frac{1}{4} . (\frac{-1}{3}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
8. \(\left(q^{\frac{-2}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{-2}{3} . \frac{2}{3} }= q^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ q^{4} }}=\frac{1}{\sqrt[9]{ q^{4} }}. \color{purple}{\frac{\sqrt[9]{ q^{5} }}{\sqrt[9]{ q^{5} }}} \\=\frac{\sqrt[9]{ q^{5} }}{q}\\---------------\)
9. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-4}{3} . (\frac{-4}{3}) }= a^{\frac{16}{9}}\\=\sqrt[9]{ a^{16} }=a.\sqrt[9]{ a^{7} }\\---------------\)
10. \(\left(q^{\frac{-5}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-5}{3} . (\frac{-1}{3}) }= q^{\frac{5}{9}}\\=\sqrt[9]{ q^{5} }\\---------------\)
11. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{3}}\\= a^{ \frac{5}{6} . \frac{1}{3} }= a^{\frac{5}{18}}\\=\sqrt[18]{ a^{5} }\\---------------\)
12. \(\left(x^{\frac{-1}{3}}\right)^{-1}\\= x^{ \frac{-1}{3} . (-1) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)