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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{1}\right)^{\frac{-1}{3}}\\= a^{ 1 . (\frac{-1}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(\left(q^{\frac{1}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{5} . (\frac{-1}{2}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
3. \(\left(a^{\frac{-4}{3}}\right)^{\frac{4}{3}}\\= a^{ \frac{-4}{3} . \frac{4}{3} }= a^{\frac{-16}{9}}\\=\frac{1}{\sqrt[9]{ a^{16} }}\\=\frac{1}{a.\sqrt[9]{ a^{7} }}=\frac{1}{a.\sqrt[9]{ a^{7} }} \color{purple}{\frac{\sqrt[9]{ a^{2} }}{\sqrt[9]{ a^{2} }}} \\=\frac{\sqrt[9]{ a^{2} }}{a^{2}}\\---------------\)
4. \(\left(y^{\frac{-5}{3}}\right)^{\frac{3}{2}}\\= y^{ \frac{-5}{3} . \frac{3}{2} }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
5. \(\left(q^{\frac{5}{6}}\right)^{\frac{-4}{5}}\\= q^{ \frac{5}{6} . (\frac{-4}{5}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
6. \(\left(y^{-1}\right)^{\frac{1}{3}}\\= y^{ -1 . \frac{1}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
7. \(\left(a^{-1}\right)^{-1}\\= a^{ -1 . (-1) }= a^{1}\\\\---------------\)
8. \(\left(y^{\frac{3}{5}}\right)^{\frac{-3}{4}}\\= y^{ \frac{3}{5} . (\frac{-3}{4}) }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
9. \(\left(x^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{3} . (\frac{-1}{2}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
10. \(\left(y^{\frac{5}{4}}\right)^{\frac{2}{5}}\\= y^{ \frac{5}{4} . \frac{2}{5} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
11. \(\left(y^{\frac{1}{3}}\right)^{2}\\= y^{ \frac{1}{3} . 2 }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
12. \(\left(x^{-1}\right)^{\frac{3}{5}}\\= x^{ -1 . \frac{3}{5} }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)