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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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