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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{3}}\right)^{\frac{2}{5}}\\= x^{ \frac{-2}{3} . \frac{2}{5} }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
2. \(\left(y^{2}\right)^{1}\\= y^{ 2 . 1 }= y^{2}\\\\---------------\)
3. \(\left(q^{\frac{-1}{6}}\right)^{\frac{5}{2}}\\= q^{ \frac{-1}{6} . \frac{5}{2} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
4. \(\left(q^{\frac{-5}{2}}\right)^{2}\\= q^{ \frac{-5}{2} . 2 }= q^{-5}\\=\frac{1}{q^{5}}\\---------------\)
5. \(\left(q^{\frac{5}{3}}\right)^{\frac{3}{4}}\\= q^{ \frac{5}{3} . \frac{3}{4} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
6. \(\left(x^{-2}\right)^{\frac{-5}{4}}\\= x^{ -2 . (\frac{-5}{4}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
7. \(\left(a^{\frac{-5}{3}}\right)^{\frac{2}{5}}\\= a^{ \frac{-5}{3} . \frac{2}{5} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
8. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-3}{4} . (\frac{-1}{6}) }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)
9. \(\left(y^{-1}\right)^{\frac{1}{3}}\\= y^{ -1 . \frac{1}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
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. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-1}{4}}\\= a^{ \frac{-1}{2} . (\frac{-1}{4}) }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)
12. \(\left(q^{\frac{4}{5}}\right)^{\frac{4}{3}}\\= q^{ \frac{4}{5} . \frac{4}{3} }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)