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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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