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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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