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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{\frac{-5}{2}}\\= q^{ -1 . (\frac{-5}{2}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
2. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-1}{4} . (\frac{-5}{6}) }= y^{\frac{5}{24}}\\=\sqrt[24]{ y^{5} }\\---------------\)
3. \(\left(q^{\frac{-2}{3}}\right)^{-1}\\= q^{ \frac{-2}{3} . (-1) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
4. \(\left(q^{\frac{5}{4}}\right)^{\frac{1}{3}}\\= q^{ \frac{5}{4} . \frac{1}{3} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
5. \(\left(a^{\frac{-5}{4}}\right)^{\frac{5}{3}}\\= a^{ \frac{-5}{4} . \frac{5}{3} }= a^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ a^{25} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a }}=\frac{1}{|a^{2}|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{3}|}\\---------------\)
6. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{4}}\\= x^{ \frac{-1}{3} . \frac{1}{4} }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
7. \(\left(q^{\frac{2}{3}}\right)^{\frac{-2}{3}}\\= q^{ \frac{2}{3} . (\frac{-2}{3}) }= q^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ q^{4} }}=\frac{1}{\sqrt[9]{ q^{4} }}. \color{purple}{\frac{\sqrt[9]{ q^{5} }}{\sqrt[9]{ q^{5} }}} \\=\frac{\sqrt[9]{ q^{5} }}{q}\\---------------\)
8. \(\left(q^{-1}\right)^{\frac{1}{4}}\\= q^{ -1 . \frac{1}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
9. \(\left(x^{\frac{4}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{4}{3} . (\frac{-1}{2}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
10. \(\left(x^{1}\right)^{-1}\\= x^{ 1 . (-1) }= x^{-1}\\=\frac{1}{x}\\---------------\)
11. \(\left(q^{\frac{-1}{2}}\right)^{\frac{5}{3}}\\= q^{ \frac{-1}{2} . \frac{5}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
12. \(\left(y^{\frac{1}{2}}\right)^{\frac{-4}{5}}\\= y^{ \frac{1}{2} . (\frac{-4}{5}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)