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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-2}{3}}\right)^{1}\\= q^{ \frac{-2}{3} . 1 }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
2. \(\left(y^{\frac{5}{3}}\right)^{\frac{-1}{4}}\\= y^{ \frac{5}{3} . (\frac{-1}{4}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
3. \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{-2}{3} . \frac{1}{5} }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
4. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-4}{5} . (\frac{-1}{2}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
5. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{3} . (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
6. \(\left(a^{\frac{4}{3}}\right)^{\frac{3}{4}}\\= a^{ \frac{4}{3} . \frac{3}{4} }= a^{1}\\\\---------------\)
7. \(\left(y^{1}\right)^{\frac{1}{3}}\\= y^{ 1 . \frac{1}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
8. \(\left(y^{\frac{-2}{3}}\right)^{\frac{1}{4}}\\= y^{ \frac{-2}{3} . \frac{1}{4} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
9. \(\left(a^{\frac{2}{3}}\right)^{\frac{3}{5}}\\= a^{ \frac{2}{3} . \frac{3}{5} }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
10. \(\left(x^{\frac{5}{6}}\right)^{\frac{3}{4}}\\= x^{ \frac{5}{6} . \frac{3}{4} }= x^{\frac{5}{8}}\\=\sqrt[8]{ x^{5} }\\---------------\)
11. \(\left(a^{\frac{-5}{2}}\right)^{\frac{5}{3}}\\= a^{ \frac{-5}{2} . \frac{5}{3} }= a^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ a^{25} }}\\=\frac{1}{|a^{4}|.\sqrt[6]{ a }}=\frac{1}{|a^{4}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{5}|}\\---------------\)
12. \(\left(x^{\frac{-2}{5}}\right)^{\frac{2}{5}}\\= x^{ \frac{-2}{5} . \frac{2}{5} }= x^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ x^{4} }}=\frac{1}{\sqrt[25]{ x^{4} }}. \color{purple}{\frac{\sqrt[25]{ x^{21} }}{\sqrt[25]{ x^{21} }}} \\=\frac{\sqrt[25]{ x^{21} }}{x}\\---------------\)