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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{2}\right)^{\frac{5}{2}}\\= q^{ 2 . \frac{5}{2} }= q^{5}\\\\---------------\)
2. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-1}{4}}\\= a^{ \frac{-2}{3} . (\frac{-1}{4}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
3. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-3}{5} . (\frac{-3}{4}) }= a^{\frac{9}{20}}\\=\sqrt[20]{ a^{9} }\\---------------\)
4. \(\left(q^{\frac{-5}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{-5}{4} . \frac{1}{2} }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
5. \(\left(a^{2}\right)^{\frac{1}{5}}\\= a^{ 2 . \frac{1}{5} }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
6. \(\left(x^{\frac{-4}{3}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-4}{3} . (\frac{-4}{5}) }= x^{\frac{16}{15}}\\=\sqrt[15]{ x^{16} }=x.\sqrt[15]{ x }\\---------------\)
7. \(\left(x^{\frac{-3}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-3}{5} . (\frac{-1}{2}) }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
8. \(\left(q^{\frac{-1}{4}}\right)^{\frac{2}{5}}\\= q^{ \frac{-1}{4} . \frac{2}{5} }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
9. \(\left(a^{\frac{1}{2}}\right)^{-1}\\= a^{ \frac{1}{2} . (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
10. \(\left(y^{\frac{1}{2}}\right)^{1}\\= y^{ \frac{1}{2} . 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
11. \(\left(x^{\frac{1}{2}}\right)^{\frac{-5}{2}}\\= x^{ \frac{1}{2} . (\frac{-5}{2}) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
12. \(\left(a^{2}\right)^{\frac{-2}{3}}\\= a^{ 2 . (\frac{-2}{3}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)