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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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