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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-4}{3}}\right)^{-2}\\= q^{ \frac{-4}{3} . (-2) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
2. \(\left(a^{\frac{-3}{2}}\right)^{1}\\= a^{ \frac{-3}{2} . 1 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
3. \(\left(x^{1}\right)^{\frac{-1}{3}}\\= x^{ 1 . (\frac{-1}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
4. \(\left(a^{\frac{-5}{4}}\right)^{-2}\\= a^{ \frac{-5}{4} . (-2) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
5. \(\left(x^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{2} . (\frac{-2}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\left(x^{\frac{-5}{3}}\right)^{\frac{4}{5}}\\= x^{ \frac{-5}{3} . \frac{4}{5} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
7. \(\left(x^{\frac{4}{5}}\right)^{\frac{-3}{5}}\\= x^{ \frac{4}{5} . (\frac{-3}{5}) }= x^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ x^{12} }}=\frac{1}{\sqrt[25]{ x^{12} }}. \color{purple}{\frac{\sqrt[25]{ x^{13} }}{\sqrt[25]{ x^{13} }}} \\=\frac{\sqrt[25]{ x^{13} }}{x}\\---------------\)
8. \(\left(y^{\frac{2}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{2}{3} . (\frac{-2}{3}) }= y^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ y^{4} }}=\frac{1}{\sqrt[9]{ y^{4} }}. \color{purple}{\frac{\sqrt[9]{ y^{5} }}{\sqrt[9]{ y^{5} }}} \\=\frac{\sqrt[9]{ y^{5} }}{y}\\---------------\)
9. \(\left(q^{\frac{-1}{4}}\right)^{\frac{1}{4}}\\= q^{ \frac{-1}{4} . \frac{1}{4} }= q^{\frac{-1}{16}}\\=\frac{1}{\sqrt[16]{ q }}=\frac{1}{\sqrt[16]{ q }}. \color{purple}{\frac{\sqrt[16]{ q^{15} }}{\sqrt[16]{ q^{15} }}} \\=\frac{\sqrt[16]{ q^{15} }}{|q|}\\---------------\)
10. \(\left(x^{\frac{3}{4}}\right)^{-1}\\= x^{ \frac{3}{4} . (-1) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
11. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{3} . \frac{1}{2} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
12. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-3}{4} . (\frac{-2}{3}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)