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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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