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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-4}{3}}\right)^{2}\\= y^{ \frac{-4}{3} . 2 }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
2. \(\left(a^{\frac{1}{2}}\right)^{1}\\= a^{ \frac{1}{2} . 1 }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
3. \(\left(q^{1}\right)^{\frac{-5}{4}}\\= q^{ 1 . (\frac{-5}{4}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
4. \(\left(y^{\frac{-3}{5}}\right)^{-1}\\= y^{ \frac{-3}{5} . (-1) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
5. \(\left(a^{\frac{-3}{2}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-3}{2} . (\frac{-3}{5}) }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
6. \(\left(x^{\frac{1}{6}}\right)^{\frac{1}{5}}\\= x^{ \frac{1}{6} . \frac{1}{5} }= x^{\frac{1}{30}}\\=\sqrt[30]{ x }\\---------------\)
7. \(\left(x^{1}\right)^{\frac{-2}{3}}\\= x^{ 1 . (\frac{-2}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
8. \(\left(q^{\frac{-4}{5}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-4}{5} . (\frac{-2}{3}) }= q^{\frac{8}{15}}\\=\sqrt[15]{ q^{8} }\\---------------\)
9. \(\left(q^{-1}\right)^{\frac{-1}{2}}\\= q^{ -1 . (\frac{-1}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(\left(x^{\frac{3}{4}}\right)^{\frac{2}{3}}\\= x^{ \frac{3}{4} . \frac{2}{3} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
11. \(\left(x^{-1}\right)^{-1}\\= x^{ -1 . (-1) }= x^{1}\\\\---------------\)
12. \(\left(q^{\frac{-1}{5}}\right)^{\frac{1}{4}}\\= q^{ \frac{-1}{5} . \frac{1}{4} }= q^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ q }}=\frac{1}{\sqrt[20]{ q }}. \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q|}\\---------------\)