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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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