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Werk uit m.b.v. de rekenregels

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

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