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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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