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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{2}{3}}\right)^{\frac{-5}{4}}\\= q^{ \frac{2}{3} . (\frac{-5}{4}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
2. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-1}{2} . (\frac{-5}{6}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
3. \(\left(y^{1}\right)^{\frac{3}{5}}\\= y^{ 1 . \frac{3}{5} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
4. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-2}{3} . (\frac{-1}{3}) }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)
5. \(\left(a^{\frac{-2}{5}}\right)^{\frac{1}{6}}\\= a^{ \frac{-2}{5} . \frac{1}{6} }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
6. \(\left(a^{\frac{-1}{2}}\right)^{\frac{1}{4}}\\= a^{ \frac{-1}{2} . \frac{1}{4} }= a^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ a }}=\frac{1}{\sqrt[8]{ a }}. \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a|}\\---------------\)
7. \(\left(y^{\frac{2}{5}}\right)^{\frac{-2}{5}}\\= y^{ \frac{2}{5} . (\frac{-2}{5}) }= y^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ y^{4} }}=\frac{1}{\sqrt[25]{ y^{4} }}. \color{purple}{\frac{\sqrt[25]{ y^{21} }}{\sqrt[25]{ y^{21} }}} \\=\frac{\sqrt[25]{ y^{21} }}{y}\\---------------\)
8. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
9. \(\left(x^{\frac{5}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{5}{3} . (\frac{-2}{3}) }= x^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ x^{10} }}\\=\frac{1}{x.\sqrt[9]{ x }}=\frac{1}{x.\sqrt[9]{ x }} \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x^{2}}\\---------------\)
10. \(\left(q^{\frac{3}{4}}\right)^{\frac{3}{5}}\\= q^{ \frac{3}{4} . \frac{3}{5} }= q^{\frac{9}{20}}\\=\sqrt[20]{ q^{9} }\\---------------\)
11. \(\left(a^{\frac{-3}{2}}\right)^{1}\\= a^{ \frac{-3}{2} . 1 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
12. \(\left(x^{\frac{-1}{2}}\right)^{-2}\\= x^{ \frac{-1}{2} . (-2) }= x^{1}\\\\---------------\)