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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{4}{5}}\right)^{\frac{-4}{3}}\\= a^{ \frac{4}{5} . (\frac{-4}{3}) }= a^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ a^{16} }}\\=\frac{1}{a.\sqrt[15]{ a }}=\frac{1}{a.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{2}}\\---------------\)
2. \(\left(y^{\frac{-5}{6}}\right)^{\frac{4}{3}}\\= y^{ \frac{-5}{6} . \frac{4}{3} }= y^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ y^{10} }}\\=\frac{1}{y.\sqrt[9]{ y }}=\frac{1}{y.\sqrt[9]{ y }} \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y^{2}}\\---------------\)
3. \(\left(x^{\frac{5}{2}}\right)^{\frac{-4}{5}}\\= x^{ \frac{5}{2} . (\frac{-4}{5}) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
4. \(\left(q^{\frac{2}{5}}\right)^{1}\\= q^{ \frac{2}{5} . 1 }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
5. \(\left(x^{\frac{5}{6}}\right)^{\frac{2}{5}}\\= x^{ \frac{5}{6} . \frac{2}{5} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
6. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{2}{3} . (\frac{-1}{2}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-3}{5} . (\frac{-4}{5}) }= q^{\frac{12}{25}}\\=\sqrt[25]{ q^{12} }\\---------------\)
8. \(\left(y^{\frac{1}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{5} . (\frac{-1}{2}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
9. \(\left(x^{-1}\right)^{\frac{5}{6}}\\= x^{ -1 . \frac{5}{6} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
10. \(\left(x^{\frac{1}{2}}\right)^{\frac{-5}{4}}\\= x^{ \frac{1}{2} . (\frac{-5}{4}) }= x^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ x^{5} }}=\frac{1}{\sqrt[8]{ x^{5} }}. \color{purple}{\frac{\sqrt[8]{ x^{3} }}{\sqrt[8]{ x^{3} }}} \\=\frac{\sqrt[8]{ x^{3} }}{|x|}\\---------------\)
11. \(\left(x^{-1}\right)^{\frac{-4}{5}}\\= x^{ -1 . (\frac{-4}{5}) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
12. \(\left(x^{\frac{1}{2}}\right)^{\frac{-3}{2}}\\= x^{ \frac{1}{2} . (\frac{-3}{2}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)